Figure - uploaded by Vesife Hatisaru
Content may be subject to copyright.
The view of function represented in the analogies (f=44).
Source publication
This study investigates the analogies used by a sample of secondary mathematics teachers when they described the concept of function. The study is concerned with understanding what analogies were used by the participant teachers and conceptions of functions positioned in those analogies. Using examples from a set of responses to five open-ended que...
Contexts in source publication
Context 1
... analogy was grouped into the views of function presented in Table 1 that they represent. Two views of function were revealed in the teachers' analogies: input-output machines; and a mapping between two sets (see Table 5). ...Context 2
... comparisons made by the teachers corresponded mostly to either the view of a function as input-output machines or a mapping between two sets (see Table 5), and these views (both refer to the correspondence approach) dominated their analogical reasoning. Some illustrative examples representing both views are presented in Table 3. Education in Science and Technology 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 ...Similar publications
According to GTR(General Theory of Relativity), the Gravity is considered as a four-dimensional curvature of space-time. And this space-time curvature is often visualized as a Rubber Sheet by some Experts. Though some people raise doubts on it. Here, In this paper, I’ve tried to give an Alternative Idea to the Rubber Sheet Analogy in General Theory...
An approach is proposed to quantify, in bits of information, the actual relevance of analogies in analogy tests. The main component of this approach is a softaccuracy estimator that also yields entropy estimates with compensated biases. Experimental results obtained with pre-trained GloVe 300-D vectors and two public analogy test sets show that pro...
Le strategie denominative di Cristoforo Colombo e Giovanni da Verrazzano seguono canoni simili: nomi che esprimono deferenza religiosa, nomi in omaggio ai finanziatori e protettori delle loro imprese, nomi suggeriti dalle caratteristiche dei luoghi, nomi legati alla sfera personale, e così via. In particolare quelli di Colombo mirano a sottolineare...
![Figure 2. Anatomy of the lymphatic system [10].](profile/Gassem-Gohal/publication/384003396/figure/fig2/AS:11431281277908078@1726323943503/Anatomy-of-the-lymphatic-system-10_Q320.jpg)
Citations
... 325). Now, studies on connections are important, but there has been no evidence of research addressing students' work on variational thinking, connections, and linear function, but rather focusing on the knowledge of high school teachers based on connections (Bingölbali & Coşkun, 2016;Hatisaru, 2022). In this line, García-García (2024) investigated mathematical understanding based on mathematical connections made by Mexican high school students regarding linear equations and functions, where he refined the framework of mathematical understanding based on connections between different representations, procedural, among others. ...
The variational thinking of high school students based on mathematical connections was analyzed through a laboratory on linear functions. This qualitative research based on design was developed in three phases: diagnostic test, implementation of the mathematics laboratory and final test, with students from a public
institution in Barranquilla, Colombia. The diagnostic test revealed difficulties in the concept of linear function and the modelling of situations. Therefore, a laboratory was implemented with eight activities focused on the concept of linear function, variation situations, generalization and conversion between different representations of the linear function (verbal, numerical, tabular, graphical, and algebraic). The results showed a significant advance in the variational thinking of the students, who managed to establish connections between different
representations, procedural, metaphorical and better understand the meanings of the linear function. Also, the type of mathematical tasks used promote mathematical connections and variational thinking about the linear function and applications.
... Rodríguez-Nieto, , for example, contributed to the advancement of the existing model for mathematical connections by introducing a novel category known as metaphorical connections (also found in Hatisaru, 2022). This addition to the model was instrumental in refining the conceptual framework, aiming to enhance the clarity and comprehensiveness of the categories within the model. ...
... In addition, 'meaning'-and meaningmaking-seems to play an implicit role in other types of connections. 'Feature/property' connections occur when a learner makes meaning of a mathematical concept; 'analogy' connections involve meaning-making links between mathematical concepts and real-world situations (Hatisaru, 2022). Is the 'meaning' type of connections so broadly conceived that it functions as an 'other' code, capturing a very broad array of types of connections that do not otherwise fall into any existing ETMC category? ...
This study investigated the mathematical connections found in the solutions provided by 22 preservice secondary mathematics teachers to a set of algebra problems. Interest in, and research on, mathematical connections has gained prominence of the past decade. Here, we use the Extended Theory of Mathematical Connections or ETMC to explore the types of connections that this framework does and does not capture in the preservice teachers' solutions. The ETMC surfaced four types of mathematical connections across four problems: 'different representations', 'procedural', 'part-whole' and 'meaning'. The other types of connections defined in ETMC such as 'reversibility' or 'feature' were not found in our data, perhaps because of the specific problems that were used. Some mathematical connections were not highlighted when examining the solutions through the lens of ETMC ('meaning', 'implication or if/then' and modelling) addressing areas in which ETMC might be limited in its capacity to support researchers in identifying mathematical connections in different contexts.
... Metaphorical connections were evident in an investigation conducted by Hatisaru (2022). The author examined teacher-made analogies to function by content analysing of a sample of 26 secondary mathematics teachers' responses to an open-ended questionnaire where they were prompted to define and exemplify the concept of function. ...
This Article Collection brings together 8 papers, whose authors have contributed to the development of the model for mathematical connections originally proposed by Businskas (2008) and extended the model to Extended Theory of Mathematical Connections (ETMC; Rodríguez-Nieto, Moll, et al., 2022). The papers in the Collection provide comprehensive empirical support for the validity of ETMC and its potential to investigate the associations between a teacher’s mathematical knowledge for teaching a concept and their ability to establish connections in teaching that concept (Hatisaru, 2023; Mhlolo, 2013). Find the Article Collection on: https://staging.www.tandfonline.com/journals/tmes20/collections/Mathematical-Connections
