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As an action research project, using mixed methodology, this study investigated how the use of math journals affected second
grade students’ communication of mathematical thinking. For this study, math journal instruction was provided. The data gathering
included pre- and post- math assessment, students’ math journals, interviews with the students, and teacher’s reflective journal.
Findings of the study indicated that the use of math journals positively influenced the students’ communication of mathematical
thinking and the use of math vocabulary. Additionally, math journals served as a communication tool between the students and
teacher and an assessment tool for the teacher. The implications of this study regarding students’ writing ability and time
constraints issues were also discussed.
KeywordsMathematical communication-Mathematical thinking-Math journal

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... Penulisan jurnal merupakan salah satu alternatif penugasan yang telah diteliti memiliki berbagai kelebihan. Di antaranya adalah melatih disposisi berpikir kritis dan kemampuan pemecahan masalah siswa (Saurino, 2008); meningkatkan pemahaman konsep matematis (Lomibao et al., 2016) serta melatih keterampilan komunikasi matematis siswa (Camahalan & Young, 2015), memiliki dampak positif kepada komunikasi matematis siswa dan penggunaan kosakata matematika (Kostos & Shin, 2010). Jurnal matematika juga dapat menjadi alat perantara komunikasi antara guru dan siswa (Kostos & Shin, 2010). ...

... Di antaranya adalah melatih disposisi berpikir kritis dan kemampuan pemecahan masalah siswa (Saurino, 2008); meningkatkan pemahaman konsep matematis (Lomibao et al., 2016) serta melatih keterampilan komunikasi matematis siswa (Camahalan & Young, 2015), memiliki dampak positif kepada komunikasi matematis siswa dan penggunaan kosakata matematika (Kostos & Shin, 2010). Jurnal matematika juga dapat menjadi alat perantara komunikasi antara guru dan siswa (Kostos & Shin, 2010). Selain itu, jurnal juga dapat menjadikan peserta didik menjadi lebih terbuka dalam mengungkapkan pendapat dan pertanyaan mereka. ...

... Tugas menulis jurnal dapat menjadi salah satu solusi untuk mengatasi hal tersebut. Beberapa penelitian menyebutkan bahwa jurnal dapat menjadi alat komunikasi antara dosen dan mahasiswa (atau guru dan siswa) (Guce, 2017;Santos & Semana, 2015;Kostos & Shin, 2010). Hal ini disebabkan karena mahasiswa dapat mengekspresikan diri dengan bebas, termasuk mengungkapkan kesulitannya dalam memahami suatu materi sampai memberi komentar terhadap pembelajaran. ...

Giving assignments as an assessment in online learning during the pandemic needs to be well-considered properly so that students are not frustrated with the piling up tasks but are unable to give educators an idea of students' concepts understanding. This qualitative study aims to describe students’ responses to assignments in the form of journal writing in the Real Analysis course. The research was conducted by asking 109 students who took the Real Analysis class to write journal. At the end of the semester, students were asked to fill out a survei to find out the student's response to the task of writing a journal. Several students were then interviewed to get a more detailed information of the responses given in the survei. The results showed that 94% of the 109 students considered journal writing assignments need to be given in the Real Analysis course. As many as 99% of students agree that the feedback given by the lecturer helps students understand the material. Finally, 94% of students agree that journal-writing assignments are effective for improving understanding in the Real Analysis course. The results of the analysis of journals written by students showed that on average, more than 80% of students wrote notes related to concepts they had previously. It shows a meaningful learning process so that journal-writing assignments can be an alternative to achieve meaningful learning, especially in online learning during a pandemic.

... Beberapa peserta didik dalam penelitian Guce menyatakan bahwa mereka tidak dapat memberitahu langsung kepada pendidik ketika menemukan kesulitaan saat memahami konsep, hal yang dianggap sulit atau menyelesaikan masalah [16]. Di antara penyebab dari masalah-masalah tersebut adalah karena peserta didik merasa takut membuat kesalahan atau malu mengungkapkan gagasan miliknya dalam menjawab pertanyaan yang diberikan [16,19]. ...

... Ketika menulis jurnal, peserta didik dapat dengan bebas mengekspresikan ide dan pemikirannya terhadap suatu materi atau pembelajaran [13,16]. Hal ini menguntungkan karena dapat membantu pendidik dapat mengetahui perasaan peserta didik terhadap pembelajaran maupun pemahaman serta proses berpikir peserta didik [19]. ...

... Namun, dalam pembelajaran daring, salah satu tantangan yang ditemukan adalah kurangnya interaksi tanya jawab atau diskusi antara pendidik dan peserta didik [1,12,20]. Jurnal matematika dapat menjadi suatu alternatif alat pendukung komunikasi antara pendidik dan peserta didik [16,19,21]. Melalui jurnal, pendidik dapat mengumpulkan informasi mengenai peserta didik dan pembelajaran, memonitor pemahaman terhadap suatu topik dan yang paling penting adalah mendekatkan pendidik dengan peserta didik [13,14,22]. ...

Kebijakan pemerintah untuk melangsungkan pembelajaran secara daring sebagai dampak dari pandemi Covid-19 mengakibatkan pendidik dan peserta didik perlu beradaptasi pada perubahan dengan cukup cepat. Hal ini memunculkan tantangan tersendiri dalam pem-belajaran Matematika. Salah satu tantangan untuk pendidik adalah memastikan setiap peserta didik memahami konsep matematis dan pendidik dapat memberikan feedback untuk kesulitan yang dialami peserta didik meskipun pembelajaran tidak dilakukan secara tatap muka. Salah satu solusi untuk mengatasi hal tersebut adalah melalui penugasan berupa penulisan jurnal matematika. Untuk mengeksplor fakta terkait penulisan jurnal pada pembelaja-ran Matematika, peneliti melakukan penelitian dengan metode Systematic Literature Review. Sebanyak 20 literatur terkait yang merupakan hasil penyaringan dari berbagai database, di-interpretasi dan dikaitkan dengan kondisi pembelajaran Matematika secara daring pada ma-sa pandemi untuk menghasilkan kajian tentang peran penulisan jurnal pada pembelajaran Matematika secara daring. Berdasarkan hasil review, peran penugasan penulisan jurnal ada-lah mampu mendukung pembelajaran matematika secara daring, yaitu meningkatkan pema-haman konsep matematis, sebagai alat refleksi diri peserta didik, mendorong peserta didik untuk mengekspresikan diri dengan bebas, perantara komunikasi antara pendidik dan peserta didik serta menjadikan peserta didik menjadi lebih terbuka dalam mengungkapkan pendapat dan pertanyaan.

... The research to date on the use of math journals in the elementary classroom is promising. First, math journals provide a means of looking into how students think and reason through problem solving but it is a task that requires explicit modeling and instruction [14,15]. Martin and Polly [15] describe a study of how three fourth grade teachers implemented a journal writing component into the instruction of two-step word problems. ...

... Second, there is emerging evidence that when math journals are combined with traditional math instruction, students' math skills improve. Kostos and Shin [14], as noted in Martin and Polly [15], similarly found that including writing as a part of math instruction enhanced performance in mathematical thinking. In Kostos and Shin's study [14], 16 second-graders participated in an action research study to measure the extent to which math journals could improve the expression of mathematical thinking. ...

... Kostos and Shin [14], as noted in Martin and Polly [15], similarly found that including writing as a part of math instruction enhanced performance in mathematical thinking. In Kostos and Shin's study [14], 16 second-graders participated in an action research study to measure the extent to which math journals could improve the expression of mathematical thinking. Data included math journals, interviews with the students and the use of teachers' reflective journals. ...

... Finally, Cohen et al. (2015) scored students' MW explanations according to a rubric where a score of 2 represented strong understanding of the mathematics, a score of 1 indicated limited understanding of the mathematics, and a score of 0 meant a response was incorrect, irrelevant, or incoherent. Additionally, at second grade, Kostos and Shin (2010) scored MW explanations according to a rubric with three categories (i.e., mathematical knowledge, strategic knowledge, and explanation). Kostos and Shin used a 0-4 scale within each category, with 4 demonstrating competence within the category. ...

... In sum, prior research in the elementary grades about MW assessments utilized different methods for scoring MW: rubric scoring (Kostos & Shin, 2010), awarding points for features of writing or mathematics (Cohen et al., 2015;, or scoring by category (Evens & Houssart, 2004). Each of these scoring methods shared similarities with scoring of general writing samples (Koutsoftas & Gray, 2012;Olinghouse & Wilson, 2013). ...

... Unfortunately, we are aware of no data from high-stakes assessments that is currently available about the MW scores of students in the late elementary grades. The more informal efforts to understand how students write about mathematics (e.g., Cohen et al., 2015;Kostos & Shin, 2010) provide detail about how students write within mathematics, and it is clear that many students struggle with MW. To improve MW knowledge, researchers have conducted several investigations. ...

High‐stakes mathematics assessments require students to write about mathematics, although research suggests students exhibit limited proficiency on such assessments. Students with LD may have difficulties with writing, mathematics, or both. Researchers employed an intervention for teaching students how to organize mathematics writing (MW). Researchers randomly assigned participants (n = 61) in grades 3–5 to receive instruction in MW or information writing. Students receiving MW outperformed control students on a researcher‐developed measure of MW (d = 1.05). Component assessment revealed MW students improved in writing organization (d = 1.49) but not in mathematics content (d = 0.11 ns). Results also indicated MW students outperformed control on percentage of correct MW sequences (d = 0.82). Future directions for MW intervention development are discussed.

... While participation in discourses and debates of mathematics for improved mathematical learning has been frequently emphasized (Burton & Morgan, 2000), formal recommendations for mathematical writing are less explicitly available (Casa et al., 2016). Despite this, studies and interventions have consistently reported the benefits of writing in learning mathematics (Fry & Villagomez, 2012;Knox, 2017;Kostos & Shin, 2010;Kuzle, 2013;Pugalee, 2001). Bangert-Drowns et al. (2004) determine that writing and learning are isomorphic to each other. ...

... With specific reference to mathematics, various studies have focused on the effects of mathematical writing in the mathematics classroom. Such research has revealed enhanced metacognitive thinking, self-confidence and enjoyment levels, which leads to increased mathematical achievement (Knox, 2017;Kostos & Shin, 2010;Kuzle, 2013;Pugalee, 2001). ...

There have been universal endorsements of the benefits of writing as an effective medium of communicating mathematically. Writing and learning are seen as isomorphic to each other and writing can facilitate the comprehension of mathematical thinking through intrapersonal communication. Through a short writing intervention, this study investigates students’ perceptions on the use of writing in the mathematics classroom and explores the impact of writing on students’ affective domains of self-confidence and enjoyment levels in mathematics. A mixed-methods approach was employed using a pre-test, intervention, post-test design for the study. Quantitative data were collected through a questionnaire adapted from the Attitudes Towards Mathematics Inventory ( Tapia & Marsh, 2004), which was administered before and after the intervention. An analysis of the quantitative data revealed a significant increase in students’ mean scores for both enjoyment and self-confidence. Qualitative data collected in the form of students’ reflections of the writing intervention indicated that, overall, students had a positive perception of writing as a means of communicating in the mathematics classroom.

... Third, educators scored MW according to specific elements (i.e., identified a mistake, provided an explanation to correct the mistake; Hebert, Powell, Bohaty, & Roehling, 2019;Kiuhara et al., 2020). Fourth, educators scored MW assessments according to rubrics with 3-, 4-, 5-, or 6-point scales to gauge aspects of MW quality (Kasmer & Kim, 2012;Kostos & Shin, 2010;Lim & Pugalee, 2004;Namkung et al., 2020). ...

... Therefore, future research should focus on examining interventions and assessments for explanatory MW. Some research has been conducted about interventions but most efforts have been focused on journal writing (e.g., Baxter, Woodward, & Olson, 2005;Glogger, Schwonke, Holzäpfel, Nückles, & Renkl, 2012;Jurdak & Zein, 1998;Kostos & Shin, 2010;Lim & Pugalee, 2004;Lynch-Davis, 2011;Tan & Garces-Bacsal, 2013) with fewer interventions using explicit modeling, practice, and feedback (e.g., Cohen et al., 2015;Hebert et al., 2019;Hughes & Lee, 2020). If students continue to participate in MW activities and exercises, more research is necessary to determine best instructional and assessment practices for explanatory MW. ...

Students in the elementary and secondary grades may use mathematics writing to express ideas and reasoning about mathematics. To understand current classroom practices related to the assessment and instruction of mathematics writing, we conducted a survey of kindergarten through Grade 12 educators across the United States who taught mathematics, with 324 respondents from 44 states. Educators expressed the primary purposes of mathematics writing included helping students learn mathematics and informing mathematics instruction. The majority of educators believed mathematics writing was important yet fewer than half regularly engaged students in instructional activities about mathematics writing. Similarly, only half of educators assessed the mathematics-writing performance of their students. A regression model used to predict the frequency of mathematics-writing activities in classrooms indicated that educators included mathematics-writing activities more frequently in their classrooms if they had higher self-efficacy for teaching mathematics writing, as well as whether they actually provided instruction in mathematics writing or assessed their students in mathematics writing.

... Several studies emphasized the necessity for interminable enhancement of mathematical thinking in education. Kostos & Shin (2010), pointed out that the communication of mathematical thinking, as well as vocabulary in Mathematics of students, is positively influenced through the use of Math journal. Hence, when implemented effectively, Math journal is one of the ways to improve the mathematical thinking of learners. ...

... Pugalee (2004), cited that journal writing is an effective tool for supporting metacognitive mathematical problem solving after comparing the consequence of the utilization of written and verbal understanding of problemsolving. Kostos & Shin (2010), investigated the journal as an assessment tool in Mathematics and their findings pointed out that journal writing improved the mathematical thinking, vocabulary, and understanding of students on the concepts of Mathematics. ...

This quasi-experimental study focused on the investigation of the
effectiveness of Math journal in the teaching of Mathematics in the Modern World
particularly in enhancing Mathematics performance among first year Bachelor of
Elementary Education students of Cagayan State University, Andrews Campus,
Tuguegarao City for second semester school year 2018-2019. This study
ascertained that journal entries in Mathematics are valuable in providing
opportunities for students to acquire substantial knowledge and coherent
understanding of Mathematics concepts by communicating their learning in their
own words. Thus, the integration of Math journal in teaching significantly
enhanced communication skills, mathematical thinking and performance of
students in Mathematics. The paper also disclosed that journal activities provide
the students with opportunities to develop a broader understanding of the
various concepts in Mathematics and learn to communicate how they feel about
the learning environment. Moreover, Math journal provides an avenue for
students to undergo the process of self-reflection and self-assessment. Hence,
through the diverse Math journal activities, the learning of Mathematics becomes
more meaningful and interesting.

... 0-7). For example, Kostos and Shin (2010) asked secondgrade students to write explanations about mathematical patterns. Students received scores according to an analytic rubric with three components: mathematics knowledge, strategic knowledge, and communication about explanations. ...

... This scoring method is another commonly used assessment to score writing (Graham et al., 2016) and has been used in the MW literature (e.g. Cohen et al., 2015;Evens & Houssart, 2004;Kostos & Shin, 2010) to examine how students write about mathematics. Advantages for the analytic scoring included: (a) it took a relatively short period of time to score, and (b) it provided more targeted information than the holistic scoring. ...

Current mathematics curricula and assessments emphasize students’ ability to communicate mathematical reasoning in writing. Limited research exists, however, on what mathematics writing (MW) is and how to assess the quality of MW. Therefore, based on our definition of MW construct, we explored 4 approaches to scoring MW: (a) holistic rubric scoring for overall quality of explanation; (b) analytical rubric scoring across 4 components (i.e., mathematics content, mathematics vocabulary, writing organization, writing grammar); (c) genre-based elements scoring (modified from the scoring form used for the Essay Composition subtest of the Wechsler Individualized Achievement Test); and (d) curriculum-based measurement mathematics-writing sequences (MWS) scoring, including rules for scoring numbers and symbols. Students from 6 classrooms in 3rd-grade, 4th grade, and 5th grade (2 classrooms at each grade level; N = 122) were recruited for the current study. Results indicated all 4 scoring methods were moderately correlated with measures of writing and mathematics. Holistic, analytic, and elements scoring were strongly correlated with each other, with slightly lower correlations for the MWS scoring. Confirmatory factor analysis further demonstrated adequate construct validity. All 4 scoring methods were reliable with an exception of lower reliability for writing components assessed by analytic scoring. Based on the validity, reliability, efficiency, and information provided by each scoring method, we recommend holistic scoring for summative assessments and elements scoring for formative assessments.

... While empirical research about non-mathematical writing is extensive (Juzwik et al., 2006), studies about mathematical writing of any type are limited (Powell et al., 2017). Where they exist, they typically examine the use of journal writing or learning logs at the end of class periods and over multiple weeks, and most have observed that there is a positive impact of writing on students' mathematical conceptual understanding (e.g., Jurdak & Abu Zein, 1998;Kostos & Shin, 2010;Cross, 2009;Atasoy & Adnan, 2020;Tan & Garces-Bascal, 2013;Meel, 1999) but not all (Porter & Massingila, 2000). A meta-analysis of the impact of mathematical writing on standardized test scores, reported an effect size of 0.42 (Bicer et al., 2018), and benefits have also been described in numerous practitioner-based journal articles (e.g., Sanders, 2009;McIntosh & Draper, 2001;Bixby, 2018, Baxter et al., 2002. ...

This chapter explores how using explanatory mathematical student writing artifacts can be used to position teachers to attend to, interpret, and respond to student mathematical thinking from an iterative and engaged stance. This chapter argues that as conceptualizations of teacher noticing shift from a view that is linear and detached to a view that is iterative and engaged, a corresponding shift should occur in the learning to notice activities that pre-service teachers engage in. The chapter proposes the idea of text clubs, and explores, with two illustrative examples, how pre-service teacher discussions that center explanatory mathematical student writing artifacts offer a potential alternative to the predominant role of video clubs that center teaching video artifacts, and how this approach may support the advancement of new paths for mathematical writing research.

... According to McLennan (2014), mathematical communication allows students to clarify and represent their understanding as well as discuss new problem-solving strategies. Kostos and Shin (2010) support that communicating mathematically contributes to the development of students' mathematical thinking and problem-solving skills. Jung and Reifel (2011) agree that communication is one of the most effective ways to improve students' conceptual understanding, problem-solving skills, mathematical reasoning and sense-making. ...

This study aimed to investigate teachers' thoughts about the role of mathematical communication in special education. Data were collected through semi-structured interviews with ten special education teachers responsible for teaching students with severe disabilities from various school levels. Data analysis used open coding to identify thematically common patterns. Results showed that special education teachers' thoughts on mathematical communication fell into six themes: (i) communicating mathematical ideas through embodiment, (ii) communicating mathematical ideas while considering cognitive competency, (iii) listening, speaking, reading, or writing mathematical language, (iv) developing positive attitudes towards using mathematical language, (v) communicating mathematical ideas through repetitions, and (vi) using mathematical language in other disciplines. Teachers have recognized that students with special educational needs require more time and effort to reach their full potential because their modes of mathematical communication can be particularly varied. Therefore, they discussed the concept of mathematical communication in special education from different perspectives and presented a number of approaches to it. Implications for future research and pedagogical practice were also discussed.

... In addition to learning software, the effect of continuity of access and use is also interesting to investigate. One way to develop students' ability to communicate mathematical thinking is to get them used to doing it continuously [43], with communication breakthroughs in interactive learning [44]. This continuity can be managed through additional supporting devices provided to students so that it occurs in terms of access and use of learning materials. ...

This study aims to use the GeoGebra application as a learning aid and ascertain the efficacy of learning videos in calculus education. Using a mathematical communication test, the research employs a quantitative approach and a quasi-experimental technique to acquire data. This study’s sample is a second-year student enrolled at a Serang-Banten university. The sample is comprised of two divisions. One class is utilized for the control group of 25 pupils and another for the experimental group of 30. In the control group, students were only taught in an online learning environment using the Zoom Meet application without explaining GeoGebra-learning videos. The findings show differences in the increase in mathematical communication skills of students who study online using GeoGe-bra-learning videos (the experimental group) and those who get online learning without using GeoGebra- learning videos (the control group). Thus, GeoGebra-learning videos are a learning support tool that can improve students’ mathematical communication skills.

... This helps the students evaluate themselves. And it enables to detect student misunderstanding in a deeper level than just giving up worksheets [10]. Consequently, it helps students think about the encountered math problem and analyzing how they can solve it [11]. ...

Students are able to elaborate and reflect on their learning if they are given the opportunity to write them down in a journal. This study assessed the effects of Journal Writing Approach on Grade 10 Students' Academic Performance and Attitude in Mathematics. It aimed to (a) describe the level of performance of students when exposed to modular learning and those exposed to modular learning with journal writing; (b) find the level of students' attitude towards Mathematics when exposed to modular learning and those exposed to modular learning with journal writing; (c) identify the significant difference of students' performance between pretest scores and posttest scores when exposed to modular learning and those exposed to modular learning with journal writing; and (d) evaluate the significant difference of students' attitude in terms of pretest scores and posttest scores i when exposed to modular learning and those exposed to modular learning with journal writing. A quasi-experimental research design was utilized in this investigation. Results showed that academic performance of both groups during the pretest were very low, and during the posttest, students exposed to Journal Writing Approach showed higher increase in post test scores. The level of students' attitude towards Mathematics for both exposed to Journal Writing Approach and without it was neutral. The group exposed to Journal Writing Approach has improved their academic performance based on the mean scores from a negative attitude in the pretest to a positive result during the posttest. But the students exposed to modular learning only remained undecided. More so, there is a significant difference on students' academic performance and attitude in Mathematics when exposed to modular learning and those exposed to modular learning with journal writing in favor of the latter. Hence, journal writing has shown positive effects in improving students' academic performance and attitude in Mathematics.

... Mathematical writing studies focused on journaling in mathematics class (Kostos & Shin 2010;Zhe 2012), using writing exercises to understand students' mathematical affect (Zhe 2012), and analysing students' mathematical writing to have greater understanding of the students' knowledge (Kuzle 2013). They argued that writing encourages students to reflect on and explore their reasoning and to extend their thinking and understanding. ...

... Students communicate mathematically in novel ways within these four mathematics-writing categories (Kostos & Shin, 2010). Students may participate in mathematics writing using a variety of methods, include journal writing (Baxter et al., 2005;Glogger et al., 2012;Lim & Pugalee, 2004), letter writing (Norton & Rutledge, 2010;Shield & Galbraith, 1998), or by responding to prompts (Cohen et al., 2015;Hughes et al., 2019;Kiuhara et al., 2020;Moran et al., 2014). ...

Increasingly, students must demonstrate knowledge in mathematics through mathematics writing, yet research lags in understanding how students engage in mathematics-writing tasks. Most available research on mathematics writing focuses on typically achieving students without considering students with mathematics difficulty (MD). In this study, we explored how students with MD who participated in a word-problem intervention randomized-control trial performed on a mathematics-writing task. We sampled 144 third-grade students with MD and evaluated student performance on an explanatory mathematics-writing measure. Overall, students with MD, on a mathematics-writing rubric with five categories, scored between 1 and 2 points out of a possible 5 points for each category. For one of the five rubric categories, Mathematics Content, the students in the word-problem interventions marginally outperformed the students in the business-as-usual condition. On average, students wrote 33.3 words, numbers, and symbols in response to the mathematics-writing prompt with an average of 8.7 mathematics vocabulary words. Of the mathematics vocabulary words used, students most frequently used formal mathematics vocabulary and names for symbolic numbers, with symbolic symbols and general vocabulary used to a lesser extent. The trends in this study will support future research to enhance mathematics-writing instruction.

... Incorporating writing in mathematics is posited to increase student achievement (Harlan, 2018); assessment scores and use of math vocabulary of students were found to increase after math journaling for five weeks (Kostos & Shin, 2010). Writing to learn is a strategy that can be employed throughout to help students be engaged and develop huge ideas and concepts; it nurtures critical thinking for it requires analysis, application, and other higher level thinking skills (Michigan Department of Education, 2009). ...

This study integrated well-designed writing assignments in the three Analytic Geometry classes of a single teacher and assessed the mathematics learning of the participants (n = 57). Marginal notes, journaling, concept maps using Frayer model and cognitive academic language learning approach (CALLA) were used as the writing activities. Mean test scores before and after the writing activities were compared. Average of the preliminary and midterm exams was encoded as the before score while that of the prefinal and final exams comprised the after score. Utilizing SPSS Version 20 and one-tailed paired-sample t-test at α = 0.05, the results (p < 0.001) revealed a significant increase in math test scores mean which is moderately attributed to the writing intervention (d = 0.5027). A significant increase in the test scores homogeneity was also observed. Well-designed writing activities seem to enhance the acquisition of mathematics and can be an effective supplement to traditional lecture math class.

... However, while empirical research about writing is extensive (Juzwik et al., 2006), studies about mathematical writing are limited (Powell et al., 2017). In general, mathematical writing studies have examined the use of journal writing or learning logs at the end of class periods and over multiple weeks, and many of these studies have observed positive impacts on students' mathematical conceptual understanding (e.g., Jurdak & Abu Zein, 1998;Kostos & Shin, 2010;Cross, 2009;Atasoy & Adnan, 2020;Tan & Garces-Bascal, 2013;Meel, 1999) but not all (Porter & Massingila, 2000). These results resonate with multiple practitioner-based accounts of the impact of mathematical writing (e.g., Baxter et al., 2002;Bixby, 2018;McIntosh & Draper, 2001;Sanders, 2009) and a meta-analysis of the impact of mathematical writing on standardized test scores, which reports an effect size of 0.42 (Bicer et al., 2018). ...

This study examines technology-enhanced teacher responses and students’ written mathematical explanations to understand how to support effective teacher responding and the centering of students’ mathematical ideas. Although prior research has focused on teacher noticing and responding to students’ mathematical ideas, few studies have explored the revisions that students make to their written explanations after teacher responding and very few explore this in authentic classroom contexts. Four high school geometry teachers and thirty of their students participated in project-based tasks examining the relationships between scale factor and the dimensions, surface area, and volume of a rectangular prism. The teachers’ written feedback and the students’ written explanations were coded and scored. Results show that student explanations improved significantly after students received feedback about their mathematical ideas. Furthermore, results indicate that the teacher feedback may be more effective if it focuses on mathematical relationships between variables and that additional feedback about the variables alone may have little impact. Results contribute to an understanding of how eliciting students’ written mathematical explanations might support effective teacher responding in classroom contexts.

... At the time that I conducted my research(2015)(2016), I could find no MMAR-specific published research studies in the social sciences or elsewhere. The samples(Craig, 2011;Glasson et al., 2006;Kostos & Shin, 2010;Sampson, 2010) cited byIvankova (2015) as MMAR exemplars, while using an approach similar toIvankova's MMAR (2015), do not actually incorporate her framework. A furtherliterature review at the time of writing this discussion (January, 2018) revealed that there have been three new articles published in the past year (2017) specifically referencing MMAR as a research methodology. ...

... Though difficult to measure quantitatively, a student's affective domain should be a primary concern for PSTs to implement practical methods that embrace effective support strategies. A mathematics teacher's role in the classroom must encompass the developmental needs of the students (Ismajli & Imami-Morina, 2018;Sead, Jelena, & Elvir, 2016;Kostelnik et al., 2015;Livy et al., 2018;Edwards, 2017;Kostos & Shin, 2010). Marshall (1994) examined the understandings of tasks that were purposeful learning by interviewing and observing kindergarten students from five classes. ...

... Recent studies which have been investigating on mathematics education reveal that it is not adequate for students to learn and use only procedural and declarative knowledge (Kostos & Shin, 2010;Lynch & Bolyard, 2012). Recent research focuses on improving higher order thinking skills instead of merely attaining and using knowledge. ...

Recent studies on mathematics education focus on improving higher order thinking skills instead of merely attaining and using knowledge. Deep understanding of mathematics requires to engage in the processes of mathematical thinking. Defining and solving problems, discovering patterns, making conjectures, inferences and justifying one's own thinking are among those mathematical processes. Using mathematical talk, discussion and discourse to promote new goals of mathematics education have been widely researched in the last decades. For these reasons, creating a classroom atmosphere which provides a fruitful communication is an important area for research in mathematics education. The purpose of the study was to implement and investigate an instructional strategy to enhance mathematical discourse among students. Students' approaches to mathematical discourse as a learning tool is also examined. Qualitative methodology was used to investigate the effectiveness of group problem solving as an instructional strategy in fostering mathematical discourse. A two hour lesson plan was developed and implemented to 20 students attending 6th grade. Students filled open-ended question forms before and after implementation. Researchers also made observations and took field notes during the implementation. Content analysis was used to analyze data. Findings of the study indicated that group problem solving is an effective way to foster mathematical discourse in the classroom. Students pointed out that they enjoy and learned from mathematical talk they engaged in this group activity. Observation and field notes also indicated if the instruction presents a problem to solve through groupwork students need to engage in mathematical talk.
Keywords: mathematical communication, mathemtical discussion, mathemtical discourse, peer learning, problem solving, mathematics education.

... Studies related to communication skills has been conducted by previous researchers (Disty et al., 2020;Klochkova et al., 2016;Kostos & Shin, 2010;Safitri et al., 2020). However, limited research has investigated the application of discovery learning model to enhance the students' communication skills. ...

p class="BodyAbstract">One way to improve students' communication skills is by applying the Discovery Learning model. It can improve students' communication skills by enabling students to express ideas of their findings. Communication skills can be orally or in writing, and teachers need to motivate students to communicate actively. This study aims to determine Year 7 students' mathematics communication skills by the Discovery Learning model in mathematics learning. This was a quantitative research using a pre-experimental design with a one-group pretest-posttest. This research population was all Year 7 students in the school studied, and the sample was one class that was selected randomly. The research instruments were pre-test and post-test to explore students' communication skills. The results indicated that the Discovery Learning model could improve Year 7 students' mathematics communication skills. It is expected that this research may inform teachers and educators concerning the application of appropriate learning model for enhancing students’ communication skills.</p

... One PST stated, "before the lesson study, I was hesitant to believe that research would help us in preparing the lessons, but after this assignment I think differently." Some of the specific references to research that the PST made in their reflections were Driscoll's (1999) Doing and Undoing, Questioning from both Reinhart (2000) and Driscoll (1999), Wait time by Reinhart (2000), Journal writing by Kostos and Shin (2010), Cooperative Learning by Johnson and Johnson (1988), Cognitive Demand by Stein et. al (2000), and articles on Lesson Study (Lewis & Tsuchida, 1998;Tolle, 2010). ...

A lesson study cycle is a professional development process that integrates research and reflection through collaboration. The cycle allows a group to refine a lesson based on these collaboration efforts such as interaction with students and the post-lesson discussion. Secondary pre-service teachers in a mathematics methods course engaged in a lesson study cycle through collaboration between in-service teachers, Georgia College professors, and students in a local high school classroom. We systematically investigated this process to determine that through preparing, enacting and reflecting on their practice, Pre-service Teachers (PST) developed insight, reasoning, and understanding of the mathematics that they taught.

... De esta forma, desarrollan la capacidad de afrontar problemas que no tengan una solución única e inminente, que es la realidad a la que se van a tener que enfrentar tanto en la vida cotidiana como en el mundo laboral (Herr, Johnson y Piraro, 2001;Common Core State Standards Initiative, 2010, p. 7). A su vez, el hecho de que haya diversidad en la resolución de los problemas ofrece la oportunidad de que el/la aprendiz comunique y analice los diversos planteamientos y métodos de resolución, dando lugar al lenguaje y razonamiento matemático, actividad fundamental analizado en los artículos (Pugalee, 2001;Jiménez, Suárez y Galindo, 2010;Kostos y Shin, 2010). Godino (2004), por su parte, también remarca que el tipo de comunicación que se da en el aula condiciona el aprendizaje del alumnado y su visión sobre las matemáticas. ...

The aim of this article is to demonstrate that through project-based learning, it is possible to develop mathematical competence and respond to curricular content. For this purpose, a qualitative study has been carried out following the case study method. The data collection techniques used are participant observation and students’ productions analysis. The project considered has been carried out with six girls and twelve boys from 6th grade of primary of Antzuola Herri Eskola school. The students agreed to assemble some aprons to cook with and they thought to work out the amount of fabric needed to make the aprons. However, due to lack of time, they only calculated the area of a sleeve. Taking this project as a reference, we demonstrate that through project-based learning, students develop the mathematical competence and the education curriculum is fulfilled.

... connections to prior knowledge and real-world experiences. Pugalee (2004) compared the use of verbal and written understanding of mathematical problem-solving and found that writing is a more effective tool for supporting metacognitive mathematical problem-solving. Through writing, a self-awareness can emerge or deepen as was shown in the study by Kostos and Shin. (2010). In their study of math journals usage with second grade students, they determined the use of math journals increased mathematical thinking, increased student use of mathematical vocabulary, and improved assessment of students' understanding of the concept. An appropriate grade benchmark for integrating writing into mathematics does not ...

... Discourse has been considered of considerable importance in teaching and learning as a means to elicit thinking processes in general and mathematical thinking in particular [4]. In developing students' mathematical thinking, communicating through questions encourage students to explain how they obtained their answer by describing their thinking process, create new solution, modify existing solution and present varied solutions [5]. However, as observed by the teacher-researchers, too much emphasis on student to student discourse the non-mathematically inclined students become confused and frustrated. ...

This study investigated the effect of explicit mathematics instruction with rigorous mathematical thinking (EMI-RMT) approach and 5E's instructional model in mathematics achievement. It utilized the quasi-experimental pretest-posttest non-equivalent control group research design to gather the data. The researchers made use of the teacher-made test with a Cronbach alpha reliability coefficient of .74. Two intact classes of freshmen education students enrolled in the school year 2018-2019 at the University of Science and Technology of Southern Philippines, Cagayan de Oro City participated in this study. One section was taught using EMI-RMT approach in discussing the concept of the plane and spherical trigonometry while the other group was taught using the 5E's instructional model. The analysis of covariance (ANCOVA) with posttest as the dependent variable and pretest as the covariate, yielded F(1,60)=.068, p=.796, which is not significant at .05 level. This implies that the achievement of students taught with EMI-RMT is comparable with the achievement of students taught with 5E's instructional model. Since many studies showed that 5E's instructional model is effective, the researchers recommend that mathematics teachers may also employ the EMI-RMT approach in their classes to improve their students' achievement in mathematics.

... Beberapa penelitian sebelumnya telah melaporkan rendahnya kemampuan komunikasi matematika siswa (Baxter, Woodward, & Olson, 2005;Heyd-Metzuyanim, 2013;Kostos & Shin, 2010). Oleh karena itu, perlu adanya pembenahan dalam proses pembelajaran matematika. ...

Abstrak:
Etnomatematika menjadi kajian tren penelitian saat ini. Etnomatematika memberikan pengaruh positif dalam pembelajaran matematika dengan melibatkan potensi budaya. Matematika perlu dikomunikasikan dengan menyisipkan budaya sehingga siswa mudah memahami materi. Oleh karena itu, etnomatematika perlu diintegrasikan dengan suatu model pembelajaran. Dengan demikian, tujuan penelitian ini adalah untuk mengembangkan perangkat pembelajaran model probing-prompting berbasis etnomatematika yang dapat melatih komunikasi matematis siswa. Penelitian ini menggunakan model pengembangan Instructional Development Institute (IDI) dengan tiga tahapan, yaitu menentukan, mengembangkan, dan mengevaluasi. Subjek penelitian adalah 30 siswa kelas 8 MTs Negeri Sidorejo Banyuwangi. Pengumpulan data dilakukan melalui angket, observasi, lembar validasi, dan tes. Perangkat pembelajaran yang dikembangkan berupa kisi-kisi soal, soal tes, LKS, dan RPP. Hasil penelitian menunjukkan bahwa perangkat pembelajaran memenuhi kriteria valid, praktis, dan efektif. Perangkat pembelajaran ini dapat digunakan guru untuk mengembangkan kemampuan komunikasi matematis siswa.
Abstract:
Ethnomatematics becomes current study trend. It gives positive influence in learning mathematics by involving cultural potential. Mathematics needs to be communicated by integrating culture so that students easily understand the material. Therefore, ethnomatematics needs to be integrated with a learning model. Thus, the purpose of this study is to develop an ethnomatematics-based probing-prompting learning device that can train student’s mathematical communication. The study used a development model of the Instructional Development Institute (IDI) with three stages, namely defining, developing, and evaluating. The research subjects were 30 eighth grade students at MTs Negeri Sidorejo Banyuwangi. Data were collected through questionnaire, observation, validation sheet, and test. The learning device consists of the prediction of test problems, test problems, student’s worksheet, and lesson plan. The result of the study shows that the learning device fulfill valid, practical, and effective criterion. The learning device can be used by teachers to develop students' mathematical communication ability.

... These facts show that Edmodo has the potential to improve student results. One way to develop mathematical thinking ability of students is to familiarize the student to do it continuously [37]. In this study, the continuity of which is in the classroom and outside the classroom (online) managed through Edmodo as a tool to support the learning of mathematics given to students so that they can drive results and motivation to learn them. ...

The objective of the study was to develop a college student worksheet using Edmodo as a learning support tool and to know the effectiveness of peer tutor learning model applied in the learning of economic mathematics on motivation and attitude. Research used for quantitative approach and quasi-experiment method to collect data applying test and questionnaire. The sample in the study is a second-year student enrolled in a college in Serang - Banten. The sample comes from two classes. One class was used for the control group of 29 students; one for the exploratory group of 40 students. In the control group, students were taught only in a personal learning environment using peer tutor models whereas experimental groups studied through peer tutor models in the classroom were supported by student worksheet learning using Edmodo. The findings show that college student worksheet's use is better than traditional learning. That is, students in the experimental group not only outperformed them in the control group in the learning outcomes, but they also showed a higher learning motivation. Although students in both groups did not differ in their attitudes toward peer tutor models, students in the experimental group expressed positive attitudes toward Edmodo. The findings of this study have implications for encouraging educators to see how technology can facilitate as a means of supporting learning and assisting learners resulting in a better atmosphere of economic mathematics learning

... When one takes into consideration the fact that the U.S. spends more per student than most countries, it is not surprising that our educational system gets a big portion of the blame. Some researchers believe that unsatisfactory student performance in the United States and other English speaking countries may be attributed to mathematics teaching practices that emphasize rote learning, memorization, and procedural knowledge (Chen et al., 2014;Edwards, 2017;Kostos & Shin, 2010;Lee & Hannafin, 2016;McLeod, 1992;Wilcox & Monreo, 2011). However, not all researchers are willing to discredit the teaching of procedural knowledge or the use of memorization strategies. ...

The purpose of the present study is to investigate pre-service teachers' previous mathematics learning experience from elementary school to college and how it relates to their attitudes and beliefs about mathematics learning and teaching. Data were collected over two semesters from a total of 67 pre-service teachers in a mathematics methods course at a mid-Western university. The results indicate that different mathematics learning tools or strategies were emphasized at different grade levels. While a few strategies that support meaningful learning showed consistent growth in their use at higher grade levels, memorization remained a heavily used strategy at all grade levels. Certain research-proven strategies (manipulatives, illustrations, measurement) were used less often at higher grade levels. Regarding the relationship between previous learning experience and current mathematics-related attitudes and beliefs, we found very limited support. Findings were discussed and educational implications were provided.

Mathematical writing is an important yet underutilized mode of discourse. Teachers play an important role in implementing and engaging their students' mathematical writing. However, research on mathematical writing does not offer suggestions for how teachers can engage students in mathematical writing. The purpose of this chapter is to contribute to this area of research by describing how teachers implemented a systematic mathematical writing intervention during a summer school program. The student writing resulting from the intervention demonstrated that students can successfully engage in mathematical writing. Further, students' written work showed key elements of mathematical writing and indicated an understanding of the subconstructs of fraction conceptualization that appeared to be absent prior to the intervention.

In this chapter, the authors situate mathematical writing within the context of discourse, define mathematical writing, describe the classroom environment that fosters mathematical writing, and share experiences engaging elementary students in mathematical writing. At their core, the types of mathematical writing are defined by the purposes for which students write in the mathematics classroom. The authors further describe the types of mathematical writing teachers prompt and are nurtured by the classroom environment. The insights shared draw from the authors' previous and current research endeavors, advancements in curriculum development, collaborations with mathematics coaches, and experiences teaching elementary students and supporting preservice and inservice teachers. They end the chapter by highlighting some directions for future research to expand our understanding of this crucial area in mathematics education.

Mathematical writing has gained attention as an essential component of discourse. Assessing and scoring students' writing pieces about mathematics has the potential to allow teachers and researchers to gain insights into the depth of students' understanding beyond what they can express orally, including their use of visual representations and symbolic notation. This chapter presents four approaches to assessing mathematical writing available in the research literature, including holistic rubric, analytic rubric, elements, and mathematics-writing sequences scoring. A description of how student writing samples were scored, and the benefits and limitations of each approach is provided. Considerations to allow teachers and researchers to make informed decisions about scoring students' writing in mathematics are provided.

While the importance of collaborative problem-solving has been highlighted as an important skill by the OECD (Organisation for Economic Co-operation and Development), no specific model exists for mathematics facilitators to implement when engaging their students in group problem-solving. In this paper, we introduce the CoPs model for Collaborative Problem-solving in mathematics, a structured approach to facilitating group-work of this kind. We outline the theoretical foundations of the CoPs model as well as its implementation in practice. We then consider its usage in a case study with 89 highly-achieving post-primary school students from numerous mixed schools around Ireland and discuss student feedback on the experience of the CoPs model as an approach to collaborative problem-solving in mathematics. Students were positive about this approach to collaborative problem-solving, suggesting that this model may provide an approach that teachers could introduce into classroom settings when teaching problem-solving in mathematics.

Komunikasi matematis merupakan salah satu cara untuk bertukar gagasan atau memperjelas pengetahuan. Komunikasi matematis memiliki tiga aspek yang berbeda. Ketiga aspek tersebut adalah komunikasi tentang matematika (communication about mathematics), komunikasi di dalam matematika (communication in mathematics), dan komunikasi dengan matematika (communication with mathematics). Selain itu, artikel ini juga membahas tiga cara yang dapat dilakukan siswa untuk berkomunikasi dengan gurunya, yaitu dengan cara lisan, tertulis, dan perilaku fisik. Standar komunikasi juga dibahas dalam tulisan ini, karena kemampuan komunikasi di setiap jenjang pendidikan tentunya berbeda-beda. Peranan komunikasi, cara mengembangkan komunikasi, dan keefektifan komunikasi penting untuk diketahui karena komunikasi yang baik akan terjadi apabila penerima pesan memahami apa yang disampaikan oleh pengirim pesan. Oleh karena itu, perlu kiranya seluruh komponen yang terlibat dalam sebuah komunikasi memainkan peranannya agar terjadi komunikasi yang baik.

Bu araştırmanın amacı, öğrenme amaçlı yazma aktivitelerinin 7. sınıf öğrencilerinin oran, orantı ve yüzdeler konusundaki akademik başarılarına etkisinin incelenmesidir. Araştırmada nicel araştırma modellerinden yarı deneysel desen kullanılmıştır. Araştırmanın örneklemini 2021-2022 eğitim öğretim yılı ikinci dönem içerisinde İstanbul ili Çatalca ilçesindeki bir devlet okulunun 7. sınıf kademesinde öğrenim gören 40 öğrenci oluşturmaktadır. Sekiz hafta süren uygulamada oran, orantı ve yüzdeler konusu ile ilgili olarak kontrol grubuna mevcut öğretim programındaki etkinlikler, deney grubuna ise öğrenme amaçlı yazma aktivitelerinden günlük tutma ve mektup yazma aktiviteleri uygulanmıştır. Deney grubundaki her bir öğrenci yedi hafta süresince toplamda 21 günlük ve yüzdeler ve oran-orantı konularından birer tane olmak üzere toplamda ikişer mektup yazmıştır. Araştırmada veri toplama aracı olarak 7. sınıf birinci dönem konularını kapsayan matematik ön bilgi testi ve oran, orantı ve yüzdeler konularını kapsayan matematik akademik başarı testi (son test) kullanılmıştır. Testlerden elde edilen verilerin analizinde SPSS programı kullanılarak bağımsız örneklem t-testi yapılmıştır. Veri analizinden elde edilen bulgulara göre uygulama sonucunda deney grubu öğrencileri lehine anlamlı bir fark ortaya çıkmıştır. Dolayısıyla öğrenme amaçlı yazma aktivitelerinden günlük tutma ve mektup yazma, 7. sınıf öğrencilerinin oran, orantı ve yüzdeler konusundaki akademik başarılarını arttırdığı sonucuna varılmıştır.

The study used the descriptive design to explore the students' mathematical creativity in terms of fluency, flexibility and originality in solving six non-routine problems. Thirty (30) participants chosen using stratified sampling from 123 Grade 10 students, were asked to solve six nonroutine problems. In each of the three sessions, two problems were answered by them, after which they were asked to write a journal about their experiences in solving a problem and then they were interviewed. Solutions of the participants which succeeded by an interview that were interpreted using validated rubrics described their mathematical creativity in terms of fluency, flexibility and originality. Results show that students may be described as "moderately creative" in all three components fluency, flexibility, originality. Likewise, the over-all level of mathematical creativity in solving nonroutine problems is moderately creative. Consequently, the researchers derived pedagogical implications to improve the mathematical creativity of students.

Peer assessment is an underutilized tool in mathematics classrooms. We examined how peer assessment could be used in a mathematics course to improve mathematical communication and mathematical proficiency. To describe in what ways peer reviews compared to teacher reviews, we analyzed ratings and feedback of 32 6th graders and their mathematics teacher. To determine what impact receiving peer versus teacher feedback had on students, we compared the revision quality and mathematical problem-solving abilities of students who received feedback from four peers to those who received feedback from their teacher. The findings indicated that middle school students can provide feedback just as helpful in improving mathematical communication and problem-solving ability as the teacher.

Mathematical communication skills are the ability to convey mathematical ideas, strategies, and solutions to solve mathematical problems, both written and verbal. The community must express ideas to solve mathematical problems in daily life or tell essential information, such as the news related to COVID-19. This research is a descriptive qualitative study that aims to describe the written and oral mathematical communication skills of 10 th-grade students, especially high achievement students, working on a PISA-like problem in the COVID-19 context. The selection of subjects in this study used purposive sampling with the subjects of 3 high achievement students in ten grade. Subjects are selected based on the average daily test scores. Data collection was conducted by mathematical communication test using PISA liked problem uncertainty and data context about hand sanitizer and interview. The triangulation technique analyzed the result of test and interview data. The results showed that students with high achievement have high mathematical communication skills. Students with high achievement can present mathematical ideas orally and in writing, interpret and evaluate the strategy, the results obtained, and use terms, mathematical notation, and math symbols. Thus, high achievement students can communicate and solve problems in the context of COVID-19. This research provides new information about the mathematical communication of students with high mathematical abilities, so it can be one of the teacher's guidelines for determining appropriate learning to improve students' mathematical communication.

The study used the descriptive design to explore the students' mathematical creativity in terms of fluency, flexibility and originality in solving six non-routine problems. Thirty (30) participants chosen using stratified sampling from 123 Grade 10 students, were asked to solve six non-routine problems. In each of the three sessions, two problems were answered by them, after which they were asked to write a journal about their experiences in solving a problem and then they were interviewed. Solutions of the participants which succeeded by an interview that were interpreted using validated rubrics described their mathematical creativity in terms of fluency, flexibility and originality. Results show that students may be described as "moderately creative" in all three components fluency, flexibility, originality. Likewise, the overall level of mathematical creativity in solving non-routine problems is moderately creative. Consequently, the researchers derived pedagogical implications to improve the mathematical creativity of students.

Mathematical communication is one of the skills that students are expected to achieve in learning mathematics. Mathematical communication can help students express mathematical ideas in their own language that can be understood by others. Students not only express mathematical ideas in a nutshell, but students must be able to explain with mathematical arguments and their reasons. This study revealed the students ‘ability in solving mathematical communication problems and identified students’ difficulties in solving mathematical communication problems. This research is a qualitative research involving 45 students of class XI. Students’ difficulties in solving mathematical communication questions were analyzed from the results of tests of mathematical communication skills and student interviews. The results showed that students still had difficulties with mathematical communication problems on the indicators of explaining mathematical ideas or situations in writing into a mathematical model, there were still many students who had not been able to solve problems that required deep thinking.

This article will focus on a study carried out during 2018/2019 academic year, within the scope of the “Supervised Teaching Practice II” of the Master in Teaching in the 1st Cycle of Basic Education and Maths and Science in the 2nd Cycle of Basic Education. The study carried out in the 2nd Cycle of Basic Education with the purpose to characterize the written communication in Mathematics of two classes of 6th grade with regard to the correction, clarity and regard to
the argumentation. Since the interpretive paradigm was associated to the main purpose of the study, qualitative methodology appeared to be more appropriate. The data were obtained through a documental collection, which included the resolutions of thirty-four students to four mathematical tasks performed in class. Frequency calculations were also used to quantify the data collected, in order to respond to the questions already mentioned. Based on the results, it was possible to conclude that the students evidenced a positive performance in their written communication in Mathematics, namely for appealing to arguments throughout their resolutions. Among the dimensions correction and clarity, it was in the first one that the students exhibited a better performance.

This study aims at analyzing students' mathematics communication ability in solving word-context problems in the topic of Linear Equation System with Two Variable and describing students' profiles in each level of mathematics communication ability in solving word-context problems in the topic of Linear Equation System with Two Variable using Polya steps. This study is a descriptive qualitative study involving 20 students of grade 8th. The data collection was conducted by using observation, test, interview, and documentation. The data analysis was conducted in three stages, namely data reduction, data display, and conclusion drawing. The results showed that: (1) Students at the low level of mathematics communication ability were only able to complete some Polya steps. The step of understanding the problem, compiling, and carrying out the plan was done poorly. Whereas the action of checking the answers was not completed. (2) Students at the level of mathematics communication ability can write down steps to understand the problem quite well. However, the stages of devising a plan, carrying out the plan, and re-checking answers cannot be done well. (3) Students at a high level of mathematics communication ability can perform the four steps of Polya even though there are still shortages in doing the calculations to get answers.

Written mathematical communication helps students in the learning process, helps teachers to assess students’ understanding, and becomes the link between the known and the written information with the understood information. The concept of understanding or procedures will be more meaningful if the students can communicate their ideas well. The study aims to describe and analyze students’ written mathematical communication abilities. This research is a qualitative descriptive study. The researchers employ tests and interviews in collecting data. The validity of the data uses the triangulation method. The results reveal that the students who have high communication ability can reach written communication indicators even though not all indicators are achieved correctly. The students who don’t have high communication ability face difficulty in expressing ideas in the form of mathematical symbols/notations so that they use meaningless notation. Meaningless notations are written based on the known information in the task and the results of students’ thinking when they experience difficulties. These students also have not been able to use algebraic expressio ns and draw conclusions correctly. They directly write the results of the answers without the procedure. They state that concluding is unnecessary. Overall, the students who have high, medium, and low ability can draw Venn diagrams even though the diagram is improper.

The aim of this study is to describe the communication ability of grade 8 students in Euclidean solid space topics based on Prior Mathematical Ability (PMA). The subject of this study consisted of 30 students. This research approach was quantitative with a descriptive method. Data collected by the test which developed based on indicators of mathematical communication. The indicators of mathematical communication used in this study are: (1) expressing a mathematical idea to the form of image; (2) expressing real objects or image to the form of mathematics; (3) state daily events in a language or mathematical symbol; (4) explain ideas, situations, and pictures in writing to mathematical form. The results showed that the average percentage of communication ability of all students was 47.68%. While the average percentage of students achieving in a high category was 62.5%. That was above the overall average of students. The average percentage of student achievement in a moderate category was 45.54%, and the percentage of students achievement in a low category was 45.00%.

Mathematical writing is one communication tool that always used by students especially when they trying to solve a problem. It becomes one of the student’s necessities to make it easier to find the right answer. It also trains students to solve problems coherently, completely, and clearly. Mathematical writing ability is important for students in Junior High School because it to know how they write the mathematical sentences in problem-solving. Teachers also need it to know how far their students can convey an answer through mathematical writing. The students’ mathematical writing ability will be measured on a particular dimension. The research method used is qualitative with the students of Junior High School as subjects. Based on the data analysis is found that on the dimension of accuracy, students are able to write answers and respond to the questions minim accuracy. On the terminology, students not use mathematical terms. In mathematical explanations, students’ explanations are minim and not thorough. It because that their written explanation is too short and minim sentences.

Purpose of the Study: The study sought to discover the level of mathematical thinking in mathematical writing among the female students of the intermediate third-level in Riyadh, and thus determine the relationship between the levels of mathematical writing and mathematical thinking among the female intermediate students of the third level. Methodology: In this research, the descriptive and analytical method is used. The analytical descriptive method was used to analyze 68 books of mathematics textbooks. The study tools consist of the mathematical writing analysis card for the records of the students and to measure their mathematical thinking. Main Findings: The development of mathematical thinking in mathematics education is the main domain of this research. Through the paper, the researcher explains the students’ mistakes in their mathematical writing. Applications of this study: The results of this study may serve to guide teachers to take care of student writing, the importance of providing a track record for students' writing and their training in the integrity of mathematical writing, showing them understanding and teaching them to provide appropriate learning. Novelty/Originality of this Study: In light of the results of the study, the researcher suggests conducting studies such as: determining the relationship between the level of mathematical writing among students and other variables such as achievement, mental ability and problem-solving. The study may also be conducted on the relationship between the teaching practices of the mathematics teachers in the mathematical communication between the students and the construction of a training program to develop the written communication among the students.

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Curriculum guidelines and professional organizations’ recommendations lack details about how often and how much students should write in mathematics and what characteristics should define their writing. This study presents an analytic framework that addresses how often students are prompted in student mathematics books to write, how much they may be encouraged to write, and the characteristics of the writing prompts. Consequently, 2,095 writing prompts in student books across 10 comprehensive Grade 3 resources were analyzed. Findings indicate a marked variation in how often and how much students are positioned to write. Most prompts have students explain what they did to solve a problem and why about number concepts, with most pressing for procedures. The greatest percentage of prompts had students write about their own solutions and do not urge them to include specific writing features.

Elementary teachers can use writing to learn effectively and regularly in their classrooms, not only to strengthen students' writing skills but also to deepen reading comprehension and encourage active learning. Students who use writing-to-learn strategies are more involved in their learning and perform better on assessments—but, more important, they develop critical thinking skills. Writing to learn provides students with safe writing opportunities, and it allows teachers to assess informally students' growth as writers and thinkers. Students who use writing-to-learn in elementary school have more opportunities to become comfortable with writing and to practice their skills before they reach secondary school, where these skills become increasingly important.This article addresses specifically use of K-W-L charts and reading journals as writing-to-learn strategies, and it provides a bibliography of trade books for science, math, social studies, and language arts that can be introduced as prompts for writing-to-learn activities.

This article considers students' classroom notebooks, their character and their role in learning. The results presented were
found within the frame work of a broader international project, the Learners Perspective Study, whose goal is to identify
classroom practice from the students' point of view. Two 8thgrade classrooms were studied. In each,every lesson over the course of three weeks was videotaped. After each lesson, two
students were interviewed and their notebooks entrees for that lesson were photocopied; once a week, the teacher was interviewed
as well. From the analysis of the data it became apparent that the notebook in the classroom is a publicobject; it is ever open for inspection and contains only finished work. That it is not a private object in which the student may freely record preliminary ideas, musings, and reflections may affect student learning negatively.
The categorization of public and private as a categorization of learning activities is discussed. The relationship between
the findings on notebooks and research on writing and classroom journals is discussed; in particular, a connection is made
between public and private domains and transactional and expressive writing,respectively.

Explanations and several examples of learning logs and discussion about the effective use of learning logs in a mathematics classroom so that students have opportunities to communicate mathematically.

The authors reassess the case for change in mathematics education and examine the objections of critics in light of recent research and evaluation evidence.

Writing during math supports students' learning as they clarify their ideas and highlight what they understand. This article presents math and writing strategies, answers to common questions, various math writing assignments, and math activities that lead to writing. (SM)

Describes a project that utilizes journal writing in the mathematics classroom. Journals are a valuable form of assessment for students and teachers and furnish concrete feedback on a student's understanding of a mathematical concept. (ASK)

The author, an experienced teacher and teacher educator, describes how she has learned to incorporate assessment purposefully into every mathematics lesson she teaches. Such an approach, she writes, tells her whether the lesson was accessible to all students while challenging the more capable, what the students learned and still need to know, how she can improve the lesson and make it more effective, and what other lesson she might offer as an alternative. The article includes strategies for assessing students' learning through written assignments and through class discussion -- for example, by asking students to explain the answers, whether or not the answers are correct; asking for more than one solution strategy; using small-group work; and asking students to restate others' ideas.

NCTM's Principles and Standards for School Mathematics emphasizes the need for all students to organize and consolidate their mathematical thinking through communication and to communicate their mathematical thinking coherently to others (NCTM 2000). Writing helps students focus on their own understandings of mathematics: “Students gain insights into their thinking when they present their methods for solving problems, when they justify their reasoning to a classmate or teacher, or when they formulate a question about something that is puzzling them” (NCTM 2000, pp. 60–61).

Innovative teachers can make writing an invaluable part of math instruction. One reason I chose mathematics for my undergraduate major was that it didn't require papers. Math homework called for solving problems or proving theorems, and that was just fine with me. Math and writing, like oil and water, seemed to have little in common. And for my first 20 years as a middle school and elementary school teacher, writing played no role in my math teaching. Today, my view has changed completely. I can no longer imagine teaching math without making writing an integral aspect of students' learning. This transition occurred over a period of years as I gradually overcame my own writing phobia. After writing children's books, professional books, and numerous articles, I've faced my writing dragon. I've even come to appreciate writing as a tool for clarifying my thinking. As Zinsser says, "Writing is a way to work yourself into a subject and make it your own" (1988, p. 16). But the results I experienced with students were what clinched my commitment to making writing a regular part of math instruction. Not only did I see how writing helped students think more deeply and clearly about mathematics, but I also discovered that students' writing was an invaluable tool to help me assess their learning.

Classroom communication figures prominently in current math reform efforts. In this study, we analyze how one teacher used writing to support communication in a seventh-grade, low-track mathematics class. For one school year, we studied four low-achieving students in the class. Students wrote in journals on a weekly basis. Using classroom observations and interviews with the teacher, we developed profiles of the four students, capturing their participation in class discussions. The profiles highlighted an important similarity among the four students: marginal participation in both small-group and whole-class discussions. However, our analysis of the students' journals identified multiple instances where the students were able to explain their mathematical reasoning, revealing their conceptual understanding, ability to explain, and skill at representing a problem. In this respect, journals potentially facilitate another important form of classroom communication. The promise of writing is that it offers an alternative to the visions of classroom communication that are strictly oral in nature.

In this article we discuss the educational value of engaging mathematics students in a specific form of writing to learn—the keeping of a journal throughout a mathematics course. As the result of an analysis which comprises both conceptual and empirical components, we suggest that journals have the potential to contribute to mathematics instruction in several ways. As the students write the journals, they can be encouraged to express and reflect upon their feelings, knowledge, processes and beliefs about mathematics, and consequently grow along each of these dimensions. By reading their students' journals, teachers may receive a wealth of information about their students and the course, and consequently improve their teaching. Finally, journals can create a new form of dialogue between the teacher and each student, thus allowing for more individualized instruction and a supportive classroom atmosphere.

This paper examines one mode of mathematical communication: that of student journal writing in mathematics. The focus of the discussion is a study of four years' use of journal writing in mathematics involving approximately 500 students in Grades 7 through 11 in a particular Victorian secondary school. The evaluation of the experimental use in one school of journal writing in mathematics provides a powerful demonstration of the link between language and mathematics and suggests a relationship between students' mathematical writings and their perceptions of mathematics and mathematical activity.

Thesis (M.A.)--Eastern Illinois University, 2000. Includes bibliographical references (leaves 77-80).

Journal writing and mathematics instruction Writing in the mathematics curriculum Writing in math class

- R Borasi
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Writing in the mathematics curriculum

- P C Burchfield
- P R Jorgenson
- K G Mcdowell
- J Rahn

Math journals boost real learning

- M Burns
- R Silbey

Writing across the curriculum: The importance of integrating writing in all subjects

- M Kelly

The reflective educator’s guide to classroom research

- N F Dana
- D Silva
- NF Dana

Issues and options in the math wars

- H L Schoen
- J T Fey
- C R Hirsch
- A F Cxford
- HL Schoen

Writing in the mathematics classroom

- C L Tuttle
- CL Tuttle