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Why we need to rehumanize mathematics

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Abstract

In this chapter, I provide an argument for why we should stop using equity as a goal and, instead, move toward rehumanizing mathematics. I provide 8 dimensions we should consider when rehumanizing mathematics teaching and learning.
... In addition to these structural influences from the social and educational contexts in which mathematics education takes place, mathematics education itself is rife with oppression. Scholars have long chronicled how structures like racism and White supremacy (e.g., Battey & Leyva, 2016;Martin, 2009Martin, , 2013Martin, , 2019Rubel, 2017;Shah, 2017;Spencer & Hand, 2015), capitalism (e.g., Gutstein, 2009;Stinson, 2004), heteropatriarchy (e.g., Boaler, 2002;Hottinger, 2016;Leyva, 2017;Mendick, 2005), ableism (e.g., Yeh et al., 2020), language discrimination (e.g., de Araujo, 2018), ethnocentrism (e.g., d'Ambrosio, 1985, imperialism (e.g., Bishop, 1990), and combinations thereof (e.g., R. Gutiérrez, 2018) pervade the histories, cultures, and practices of mathematics education as it is typically enacted, systematically privileging some students and disenfranchising others. Scholars have also documented how mathematics educators often adhere to narrow definitions of mathematical activity and mathematical ability (Louie, 2017; see also Boaler & Greeno, 2000;Cobb & Hodge, 2011;Horn, 2007;Nasir et al., 2008). ...
... In looking beyond the boundaries of the present and beyond the boundaries of the school, critical bifocality draws our attention to the cumulative and overlapping effects of small things: how negative interactions with one teacher, one policy, or one institution accumulate over time, producing, for example, systemic dehumanization of Black girls (Joseph et al., 2019). They add up to what Rochelle Gutiérrez (2018) terms the "slow violence" of mathematics education, and what Martin et al. (2019) categorize as physical, symbolic, and epistemological violences. Consequently, as Weis and Fine (2012) argued in their invocation of critical bifocality, so-called sweet spots of refuge-however sweet and significant they may be-can never be immune to, nor inoculate students against, the circulation of violence so long as society is organized by oppressive structures. ...
Article
Education researchers have long wrestled with the interplay of oppressive structures and individual agency in reproducing, sustaining, and contesting marginalization. In this article, we suggest that Weis and Fine’s construct of critical bifocality may assist researchers in understanding and addressing marginalization in mathematics education. We conduct a conceptual review of existing mathematics education literature that accounts for both structure and agency in theorizing marginalization. By reading this literature alongside Weis and Fine’s 2012 article, we develop four criteria for operationalizing critical bifocality in mathematics education research. The findings from this review highlight the interconnectedness of structures and individual lives, of the material and ideological elements of marginalization, of intersectionality and within-group heterogeneity, and of histories and institutions. Additionally, they offer theoretical and methodological recommendations for researchers studying marginalization in mathematics education.
... The low local levels in (Iraq) in recent years compared to the progress of international levels may be due to the weak codification of the training programs applied, especially those that depend on building their exercises on the mechanical conditions accompanying the kinetic technical performance of the thrower, including the peripheral velocity of the joint point of the driving arm of the group and the basic kinematic variables related to the moment The shot is released from the player's hand, through which the forward horizontal distance (the archer's Shot put result) is determined [29]. And through a simple comparison of the levels recorded in Olympia, continental and worldwide, which exceeded meters in most international tournaments for the first-placed holders in each championship, as well as the (Iraqi) record recorded more than twenty years ago, of (18.36 m) for the hero Khaled Muhammad Wajih, with the numbers recorded in the last two decades and not exceeding meters for the Iraqi champions in local and international championships, the Iraqi digital low level is undoubtedly evident, that the great decline may be due to the weakness of training programs, which may be limited only by relying on the development of some physical abilities and old methods of developing performance skills The technical and also the qualitative analysis by the coach, which is not commensurate with the size of the great scientific progress that the modern training process has reached, which depends on building its exercises on the foundations and values of biomechanical kinematic analysis programs, and also that the proper and early selection of novice athletes may predict the project of an upcoming champion, and this is what It is produced by the results of scientific research, especially those that depend on the values of the special mechanical variables in the final payment phase of the batch, in addition to the physical capabilities and specifications that it has Suitable [29,30,31]. Due to the importance of this competition internationally and its place among other games, especially track and field competitions, the researchers decided to conduct this study, to avoid some of the weaknesses of novice athletes in the future and to enhance and develop the positive points, and thus contribute to the development and improvement of the Shot put result. ...
... This requires the player to be strong and flexible limbs because it contributes significantly with the rest of the physical and mechanical variables to increase the shot speed from the putter's hand to the moment of the final push and through the occurrence of a reverse reaction to the movement of the hip at the moment of stopping due to the large resistance arm represented by the limited front movement [30]. The angle of release is an influential factor in achieving the longest horizontal distance forward that the shot puts, especially if the other basic mechanical conditions in the throwing process are met with it, which is the launch speed that has to do with the horizontal velocity of the player, which he acquires through the kinetic transfer of his center of gravity within the throwing circle towards the throwing sector, and with height The Release point [29]. ...
... The low local levels in (Iraq) in recent years compared to the progress of international levels may be due to the weak codification of the training programs applied, especially those that depend on building their exercises on the mechanical conditions accompanying the kinetic technical performance of the thrower, including the peripheral velocity of the joint point of the driving arm of the group and the basic kinematic variables related to the moment The shot is released from the player's hand, through which the forward horizontal distance (the archer's Shot put result) is determined [29]. And through a simple comparison of the levels recorded in Olympia, continental and worldwide, which exceeded meters in most international tournaments for the first-placed holders in each championship, as well as the (Iraqi) record recorded more than twenty years ago, of (18.36 m) for the hero Khaled Muhammad Wajih, with the numbers recorded in the last two decades and not exceeding meters for the Iraqi champions in local and international championships, the Iraqi digital low level is undoubtedly evident, that the great decline may be due to the weakness of training programs, which may be limited only by relying on the development of some physical abilities and old methods of developing performance skills The technical and also the qualitative analysis by the coach, which is not commensurate with the size of the great scientific progress that the modern training process has reached, which depends on building its exercises on the foundations and values of biomechanical kinematic analysis programs, and also that the proper and early selection of novice athletes may predict the project of an upcoming champion, and this is what It is produced by the results of scientific research, especially those that depend on the values of the special mechanical variables in the final payment phase of the batch, in addition to the physical capabilities and specifications that it has Suitable [29,30,31]. Due to the importance of this competition internationally and its place among other games, especially track and field competitions, the researchers decided to conduct this study, to avoid some of the weaknesses of novice athletes in the future and to enhance and develop the positive points, and thus contribute to the development and improvement of the Shot put result. ...
... This requires the player to be strong and flexible limbs because it contributes significantly with the rest of the physical and mechanical variables to increase the shot speed from the putter's hand to the moment of the final push and through the occurrence of a reverse reaction to the movement of the hip at the moment of stopping due to the large resistance arm represented by the limited front movement [30]. The angle of release is an influential factor in achieving the longest horizontal distance forward that the shot puts, especially if the other basic mechanical conditions in the throwing process are met with it, which is the launch speed that has to do with the horizontal velocity of the player, which he acquires through the kinetic transfer of his center of gravity within the throwing circle towards the throwing sector, and with height The Release point [29]. ...
Article
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Purpose: Predicting the selection of emerging shot put athletes is important in creating a new champion in International competitions. As in other games, the peripheral velocity and the main mechanical kinematic variables at the moment of firing play an important role in determining the horizontal distance. The purpose of this study is to determine the correlation of the mechanical variables (understudy) and their contribution ratios and also to know its prediction equation in the selection process. Material and method: This study was based on a sample of 9 students from the fourth stage, Division 1, for the academic year 2017/2018 at the Faculty of physical education, University of Maysan. The data obtained in the study were given as arithmetic mean, standard deviation, median, skew coefficient, Pearson correlation coefficient, analysis of variance and linear regression, constant term, standard error. Results: The researchers used the descriptive and analytical approach due to its relevance to the nature of the research, and the most important results were knowledge of the predictive equation, correlational relationships, and their contribution rates in determining the achievement of the novice player in the shot put competition. Conclusion: The basic prediction equation that determines the expected performance in the selection of junior athletes in the shot put is recommended according to the high reliability of the results obtained, and it is advisable to use these characteristics to evaluate novice players and build and create champions in this competition. Keywords: The predictive value, the numerical level, beginners athletes, shot put. Introduction The shot put is a field event in athletics and each of the events has a specific set of features including the characteristics of the implement used (size weight and aerodynamic qualities), space limitations, and technique requirements which influence the sequence of events and make them unique [1,2]. The goal in the throwing events is to maximize the measured distance covered by the implement and this distance is determined by several parameters such as height, velocity, angle of release [3,4], aerodynamic qualities, and environmental factors [5,6], exploitation of the escape space when the equipment is thrown out and temporary foot position [7,8]. The release height is a consequence of the athlete's length of the body, length of arm; body mass and it is a prerequisite for a candidate's selection for shot-putting. [1,9]. The release angle depends on the release height and the release velocity [3,10]. The angle of the release is smaller, the higher the height and the speed of the throw [11]. It is relatively constant for an individual athlete and cannot be changed to improve the result. The release velocity is by far the most important of all the release parameters in determining the distance achieved because the distance is proportional to the square of the release velocity [6,12]. The shot put competition is one of the athletics activities that is included in the international competitions like the Olympic Games, World Track & Field competitions, and continental Sports meet. Its skill performance is based on the same as other competitions due to mechanical conditions in its performance, despite the difference in the method or style of performing the movement before the final release of the shot. The analysis is the sorting and tabulation of the many data with its main elements, then logically treating them with a balance, with an appropriate standard and axis to shift from their precise quantitative formulas to others with meaningful explanations to solve the problem addressed by the researcher [13]. Biomechanical Knowledge is a "Must" for Coaching, and all movements of men and animals are determined by the laws of mechanics. It is the first task of science is to understand the movements of athletes; therefore it is an indispensable base for coaching. In the throwing events, the factors influencing the performance are governed by the physical laws of the flight phases of the implement and the biomechanical laws of the movement of the system, putter, and implement' before release [14]. Projectiles obey constant acceleration, making them easier to describe and understand (Galileo's equations). Three factors determine trajectory, including horizontal displacement, of a projectile speed of release, angle of release, the height of release. Positive height of release, the optimal angle should be slightly lower than 45°. Theoretically, the optimal angle is about 40-41°, skilled shot-putters use angles of 35-37° [3]. Shot-putting requires great explosive strength, together with the
... The low local levels in (Iraq) in recent years compared to the progress of international levels may be due to the weak codification of the training programs applied, especially those that depend on building their exercises on the mechanical conditions accompanying the kinetic technical performance of the thrower, including the peripheral velocity of the joint point of the driving arm of the group and the basic kinematic variables related to the moment The shot is released from the player's hand, through which the forward horizontal distance (the archer's Shot put result) is determined [29]. And through a simple comparison of the levels recorded in Olympia, continental and worldwide, which exceeded meters in most international tournaments for the first-placed holders in each championship, as well as the (Iraqi) record recorded more than twenty years ago, of (18.36 m) for the hero Khaled Muhammad Wajih, with the numbers recorded in the last two decades and not exceeding meters for the Iraqi champions in local and international championships, the Iraqi digital low level is undoubtedly evident, that the great decline may be due to the weakness of training programs, which may be limited only by relying on the development of some physical abilities and old methods of developing performance skills The technical and also the qualitative analysis by the coach, which is not commensurate with the size of the great scientific progress that the modern training process has reached, which depends on building its exercises on the foundations and values of biomechanical kinematic analysis programs, and also that the proper and early selection of novice athletes may predict the project of an upcoming champion, and this is what It is produced by the results of scientific research, especially those that depend on the values of the special mechanical variables in the final payment phase of the batch, in addition to the physical capabilities and specifications that it has Suitable [29,30,31]. Due to the importance of this competition internationally and its place among other games, especially track and field competitions, the researchers decided to conduct this study, to avoid some of the weaknesses of novice athletes in the future and to enhance and develop the positive points, and thus contribute to the development and improvement of the Shot put result. ...
... This requires the player to be strong and flexible limbs because it contributes significantly with the rest of the physical and mechanical variables to increase the shot speed from the putter's hand to the moment of the final push and through the occurrence of a reverse reaction to the movement of the hip at the moment of stopping due to the large resistance arm represented by the limited front movement [30]. The angle of release is an influential factor in achieving the longest horizontal distance forward that the shot puts, especially if the other basic mechanical conditions in the throwing process are met with it, which is the launch speed that has to do with the horizontal velocity of the player, which he acquires through the kinetic transfer of his center of gravity within the throwing circle towards the throwing sector, and with height The Release point [29]. ...
Article
Full-text available
Purpose: to determine the most significant kinematic indicators in the sports selection of beginner shot putters. Material and Methods: This study was carried out on a sample of 9 students at the fourth stage of the competition in Division 1, which took place in the 2017/2018 academic year at the Faculty of Physical Education of Maysan University. The following kinematic (biomechanical) parameters were analyzed: the angle of release of the nucleus, the velocity of release, the height of the point of ejection of the nucleus and the speed of swing. The correlation coefficients were determined between the kinematic indicators and the result in the shot put, as well as the regression equation for the dependence of the result in the shot put on the knematic indicators. The data obtained in the study were presented in the form of the arithmetic mean, standard deviation, median, skewness coefficient, Pearson's correlation coefficient, analysis of variance and linear regression, which included the contribution coefficients of each analyzed indicator, standard error, reliability of the regression equation as a whole, and reliability of the coefficients contribution to the shot put result of each kinematic exponent. Results. It has been shown that the swing speed has the greatest influence on the result in the shot put among beginner athletes. The swing speed, shot angle, shot speed and shot height have significant relationships with the shot put result. The multiple regression equation for the dependence of the shot put result on the swing speed, shot angle, shot height and shot point turned out to be reliable in general. However, only the swing speed has a reliable coefficient of the regression equation. The shot angle tends to be the determining factor in the shot put result. The release rate and the height of the release point have significant correlations with the shot put result, although in the regression equation they have unreliable indicators of influence on the shot put result. Conclusions. When teaching beginner shot putters, the greatest attention should be paid to the pushing swing technique, namely the swing speed. The second most important indicator is the angle of the shot put, it is recommended to use the basic prediction equation, which determines the expected results in the selection of young athletes in shot put, with high reliability of the results obtained. These characteristics are recommended to be used for evaluating young athletes, as well as in the process of training and preparing athletes for competitions.
... While the college and department have explicit diversity action plans and statements, and despite awareness of various department and institution DEI initiatives, the three department leaders shared very different visions of equity and equitable teaching. This embodies Gutiérrez's (2002Gutiérrez's ( , 2017Gutiérrez's ( , 2018 description of the word equity as being complicated by a long history of conceptualization. In her work, she shares that this often results in the word equity retaining simplistic or superficial definitions that refer to a wide range of meanings and contexts that have led many to believe that they are speaking of the same ideas/topics despite having different definitions. ...
Conference Paper
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In the wake of national movements calling for attention to equity, colleges, departments, and instructors are now faced with various responsibilities to implement practices and structures to support diversity, equity, and inclusion (DEI). This project aims to design a professional development program for mathematics graduate teaching assistants (MGTAs) by helping them learn evidence-based teaching practices to support diverse groups of learners in engaging mathematics activities. Part of these efforts included investigating department leaders' understanding of equity. This paper focuses on interviews with department leaders at a large, public, research university. Our analysis shows that despite the implementation of university structures focused on improving equity, department leaders had very different understandings of equitable teaching, and reported differences in how equity factors into their roles.
... Rehumanizing mathematics We wish to elevate how Ms. M rehumanized mathematics (in the sense of Gutiérrez, 2018) for her students throughout these episodes. She sought to create robust learning opportunities using the cognitive tools students brought to her classroom, centering classroom discussion around student-created representations, and working to build shared understanding and appreciation of each others' WoU. ...
Article
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In this case study, we investigate one teacher’s implementation of DNR-based combinatorics curriculum in their high school discrete mathematics class. By examining the teacher’s practices in whole-class discussions of two counting problems, we study how they advanced a variety of ways of thinking to support the development of a set-oriented way of thinking about counting. In particular, we find the teacher worked to build shared experience and understanding of mathematical ideas by grounding her teaching in students’ ways of understanding and leveraging students’ intellectual needs. In doing so, the teacher promoted a set-oriented way of thinking through attending to connections between sets of outcomes, counting processes, and formulas in student representations and justifications; elevated solutions employing process pattern generalization; and advanced the beliefs that counting problems can be solved in many ways and entail several types of mathematical activity.
... Interpersonal engagement is considered central in the sociocultural learning theory [5][6][7] and fulfills basic psychological needs to feel connected and to belong in a learning community [8]. This engagement is particularly important for supporting women and students of color to forge STEM identities [9] and persist in STEM fields [10][11][12]. Schools and educators across the world undertook efforts to adapt to rapidly changing circumstances of COVID-19 and to support their students through academic and life challenges [1]. However, little empirical research has studied the specific instructional methods that instructors used to adapt to the ever-changing circumstances of the pandemic and how these practices affected under-represented groups of students' belonging to critical transition classes in STEM. ...
Article
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The COVID-19 outbreak spurred unplanned closures and transitions to online classes. Physical environments that once fostered social interaction and community were rendered inactive. We conducted interviews and administered surveys to examine undergraduate STEM students’ feelings of belonging and engagement while in physical isolation, and identified online teaching modes associated with these feelings. Surveys from a racially diverse group of 43 undergraduate students at a Hispanic Serving Institution (HSI) revealed that interactive synchronous instruction was positively associated with feelings of interest and belonging, particularly for students of color, while noninteractive instruction reduced social belonging, but was related to more cognitive engagement. Small group and one-on-one interviews with 23 of these students suggest that students derived feelings of connectedness from their instructors, peers, and prior experiences and relied on their sense of competency to motivate themselves in the course and feel a sense of belonging. Two embedded cases of students in physics classrooms are compared to highlight the range of student feelings of connectedness and competency during the lockdown. Findings reaffirm that social interaction tends to support belonging and engagement, particularly for under-represented (Black or African American and Hispanic) racial groups in STEM. STEM instructors who aim to support feelings of belonging and engagement in virtual learning environments should consider increasing opportunities for student–student and student–teacher interactions, as well as taking a flexible approach that validates and integrates student voice into instruction. Future research is needed to further explore the themes of relatedness and competency that emerged as aspects of course belonging.
... As mathematics becomes a more essential part of STEM classes and topics, these children can lose interest in STEM or doubt that they have the ability to pursue a STEM-related career (Cohen & Kelly, 2020;Dika & D'Amico, 2016;Jiang et al., 2020). To make matters worse, math in school is often portrayed as a disconnected set of formulas or procedures that have little to do with the creative, flexible ways that math is used in both STEM and our daily lives (Gutiérrez, 2018;NCTM, 2018;Pattison et al., 2017). ...
Article
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Making experiences and activities are rich with opportunities for mathematical reasoning that often go unrecognized by both participants and educators. Since 2015, we have been exploring this potential through the Math in the Making initiative. The work focuses particularly on children’s museums and science centers, many of which have developed maker spaces and programs over the last decade. In this article, we share insights from our most recent round of research. To begin, we consider the fundamental question of what it means to authentically integrate mathematics with making.
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Chapter to appear in Voigt, M., Hagman, J. E., Gehrtz, J., Ratliff, B., Alexander, N. & Levy, R. (Eds.). (Submitted). Justice through the lens of calculus: Framing new possibilities for diversity, equity, and inclusion. Mathematical Association of America.
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In this volume, we encouraged a broad array of submissions that highlight issues of Diversity, Equity, and Inclusion (DEI) in introductory mathematics programs with special attention to precalculus, differential calculus, and integral calculus and surrounding departmental programs to support students in these courses. The volume features illustrative case studies that showcase ways in which departments and instructors are attending to promoting diverse introductory mathematics programs, achieving, or monitoring equitable student outcomes and experiences, and promoting inclusive teaching practices. Achieving and promoting DEI issues in introductory mathematics programs is not an easy undertaking so we encouraged submissions of models in progress, discussions of potential obstacles, challenges, and what departments and instructors have done to overcome barriers to address these issues. The volume also features thematic chapters that create a vision for DEI based on the illustrative case studies and known literature.
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