Search Results

In my study of equity in mathematics learning spaces this summer, I utilize the case of Mukuru kwa Njenga to design an iSTEM lesson to provide my students with a unique opportunity to learn. Through exploring the concept of algebraic functions, optimization using inequalities, and real-world applications, I intend to foreground social justice issues that resonate with the challenges faced by the residents of this Kenyan shantytown and other informal and downtown settlements across the globe. By intertwining mathematics and social justice, my goal is to foster a deeper understanding of algebraic functions and their applications and empower my students to become agents of change. Mukuru kwa Njenga served as a compelling context to exemplify the deplorable conditions and challenges residents of informal settlements face worldwide. The community faces numerous socioeconomic disparities, including inadequate housing, limited access to education and healthcare, and environmental risks (UN-Habitat, 2020; Wamukoya et al., 2020). By examining these challenges through the lenses of social justice mathematics, my students would develop a more nuanced understanding of how mathematics can be applied to address real-world problems. Through our study, we aimed to instill a sense of social responsibility and awareness in my students. By analyzing the inequalities present in Mukuru kwa Njenga and proposing mathematical solutions, they would gain valuable insights into the power of mathematics as a tool for social change. Our work will not only expand their mathematical skills but also nurture their empathy and critical thinking abilities, preparing them to contribute meaningfully to creating a more equitable society. By incorporating the case of Mukuru kwa Njenga into my study, I aimed to bridge the gap between mathematics education and social justice. Through this holistic approach, my students will be able to grasp the profound impact mathematics can have on addressing real-world issues and promoting social equity. Below are some videos exemplifying some of the challenges and segregation experienced in different parts of the world. The Challenges Caused By I-81 in Syracuse City NY Segregated Syracuse KBC Channel 1 Report on the Mukuru Kwa Njenga Plight References UN-Habitat. (2020). Urban slums report: The case of Nairobi, Kenya. United Nations Human Settlements Programme. Wamukoya, G., Kadengye, D., & Mbatha, R. (2020). Environmental management in informal settlements: The case of Mukuru kwa Njenga, Nairobi, Kenya. Environment and Urbanization Asia, 11(1), 71-88.

This semester has been eventful; my research interest has been tweaking and focusing more on mathematics educator identities and the identities available for students in reflective mathematics classroom discourse. It's interesting to listen to conversations surrounding student math conceptualization in differing learning environments, be it Holland's et al. (1998) figured worlds or Tate's (2008) geospatial factors. My interest in and about figured worlds is due to differential learning outcomes witnessed across the USA or even in my home country Kenya (Anderson & Ritter, 2020). I have always wondered why math educators given the same training and students at the same level would produce different results. I have appreciated Yackel and Cobb's (1996) observation that we can not separate an individual's learning from their social and cultural interactions. I also find Holland's et al. (1998) argument about socioeconomic, sociopolitical, cultural, and ideological backgrounds helpful in understanding Rubin (2007) and Urieta (2007) as they explicate how other discourses affect in-class discourses. Hogrebe and Tate's (2012) and Duncan-Andrade & Morrell, 2008 work point to racialized social and political systems that have failed to differentiate learning opportunities. Fonger (2021) joined Kendi (2019); Levya (2021); and Berry et al., 2015 in calls to dismantle whiteness and patriarchy in mathematics learning and doing space. Through Fonger's work with the antiracist algebra coalition of changing educators' perception of black students, I see the sense of Graven and Heyd-Metzuyanim (2019); and Shabtay and Heyd-Metzuyanim (2019) as framed from Holland's et al. (1998) and Shulman's (1986) works in preparing novice educators' professional identities. My exploration over the semester has helped to ground me in the humanistic theoretical framework situating mathematics teacher education at the core of classroom discourse. While students are the focus of knowledge development through humanist lenses, educators' professional identities are essential in availing learning and struggling opportunities for the students. I have explored classroom discourse from student and teacher identities, math classroom norms, math educator development, and how all these might impact classroom discourse. I find this progressive in my pursuit to understand the causes of differential learning and how figured identities could apply to its solution. References Anderson, K. P., & Ritter, G. W. (2020). Do school discipline policies treat students fairly? Evidence from Arkansas. Educational Policy, 34(5), 707-734. Battey, D., & Leyva, L. A. (2016). A Framework for Understanding Whiteness in Mathematics Education. Journal of Urban Mathematics Education, 9(2), 49-80. Duncan-Andrade, J. M. R., & Morrell, E. (2008). The art of critical pedagogy: Possibilities for moving from theory to practice in urban schools (Vol. 285). Peter Lang. Fonger, N. L. (2021). A Heart-Centered Stance: Receptivity to Algebra Teachers’ and Students’ Multidimensional Experiences. Journal of Humanistic Mathematics, 11(1), 225-264. Graven, M., & Heyd-Metzuyanim, E. (2019). Mathematics identity research: The state of the art and future directions. ZDM, 51(3), 361-377. Heyd-Metzuyanim, E., & Shabtay, G. (2019). Narratives of ‘good instruction: Teachers’ identities as drawing on exploration vs. acquisition pedagogical discourses. ZDM, 51(3), 541-554. Hogrebe, M. C., & Tate IV, W. F. (2012). Geospatial perspective: Toward a visual political literacy project in education, health, and human services. Review of Research in Education, 36(1), 67-94. Holland, D., Lachicotte Jr, W., Skinner, D., & Cain, C. (2001). Identity and agency in cultural worlds. Harvard University Press. Kendi, I. X. (2019). How to be an antiracist. One world. Leyva, L. A. (2021). Black women’s counter-stories of resilience and within-group tensions in the white, patriarchal space of mathematics education. Journal for Research in Mathematics Education, 52(2), 117-151. Rubin, B. C. (2007). Learner identity amid figured worlds: Constructing (in) competence at an urban high school. The Urban Review, 39(2), 217-249. Shulman, L. (1987). Knowledge and teaching: Foundations of the new reform. Harvard educational review, 57(1), 1-23. Tate, W. F. (2008). Putting the" Urban" in mathematics education scholarship. Journal of Urban Mathematics Education, 1(1), 5-9. Urrieta, L. (2007). Identity production in figured worlds: How some Mexican Americans become Chicana/o activist educators. The Urban Review, 39(2), 117-144. Yackel, E., & Cobb, P. (1996). Sociomathematical norms, argumentation, and autonomy in mathematics. Journal for research in mathematics education, 27(4), 458-477. The ground we must cover as educators to make learning happen in our classes

Fall 2022, my first semester as a boilermaker, has seen a beehive of activities. I have attended a number of workshops running from general orientation to specific departmental workshops punctuated with mentorship luncheons and dinners. I recount the most recent mentorship luncheon where one of my good professors, assisted by some senior graduate students, facilitated a graduate mentorship luncheon. This meeting brought together mentors and mentees to listen to the report from a recent survey and scaffold any new ideas on graduate student mentorship. The hosts served us a meal that had a touch of a typical local lunch spiced with leafy portions, chicken, and rice; not sure what the other pieces were, but I enjoyed the sumptuous lunch. The ambiance and ground rules were well articulated even though not verbalized, movement and facial connectivity took center stage in harmonizing these. My greatest takeaway was the openness of faculty mentors who expressed their frustration with the time and lack of motivation. The report indicated that some faculty have as many as nine mentees, whom they have to meet their expectations irrespective of which sub-departments they come from, let alone the lack of instantaneous information they could share at a click. I was amazed at the suggestions of centralizing information about graduate programs, the onboarding process, housing, and other activities that support graduate students. But this was far from my interest; my intention of attending workshops was to observe the dynamics of interactional webs (Gee, 1999); it was interesting to see how power positioned the mentors and how it shaped and constrained mentees’ contribution to the overall discourse (Rubbin, 2007). Mentees’ contributions were affected by their figured identities, social, cultural, and ideological backgrounds, and self-will and beliefs about expressing themselves before their seniors (Holland et al., 1998). Members of our table whose mentor was present were too careful not to mention what would provoke their mentor. They always sort for affirmation before any further ventilation. I am convinced that situation and power decide how much our identity will be displayed or operationalized. Taking this to the classroom, teachers must redefine their relationships with the students so that everyone will appropriately be positioned and empowered to participate in ensuing classroom discourse. The event was a big success. I look forward to more workshops to continue scaffolding interactional webs. A web-like Interaction Patterns

It's the second week since I got my assignment to one good professor as a research assistant. I had never experienced an elementary class session in the near past, to be precise, here in the US. My assignment for the day was to accompany the professor to a grade 5 class where he is currently collecting data to respond to the urgency of conceptions and perceptions of teachers about integrated STEM in the elementary school curriculum and how this might impact classroom discourse. The day's activity was hands-on, but that wasn't my concern. My conscience was preoccupied with a comparative study; I imagined a grade 5 class teacher trainee I assessed back in Kenya in the year 2020; I did not look at classroom (dis)organization, student numbers, learning materials, or level of rigor. My concentration was on teacher-learner and learner-learner positioning in classroom interactions (Kayi-Ayda & Miller, 2018; Rubbin, 2007). While the new Kenyan elementary school curriculum heavily borrowed from the first economies, there was a jungle of differences between what the teacher and the students embodied in this class before interacting with the learning resources. The teachers' content and pedagogical content knowledge lay a foundation for professional identity, creativity, and the decomposition of the object of learning besides their belief system. The teachers then position themself in the classroom as winners of the student's confidence. The student's beliefs, culture, and ideologies summed up my observations. While they had watched the same videos and given similar instructions, each group used different geometrical shapes to provide tensile support on a bridge. The best groups improvised the over-support in addition to the two recommended under-supports. These students did not look at the technical challenges in designing a bridge but positioned themselves as site engineers and produced different prototypes of bridges. The classroom discourse was organic, and every learner openly shared their challenges, learning points, and what they could do differently next time. The teacher's conceptions and perceptions of integrated STEM position them in a predominantly productive position in the class. It gives them the impetus to plan, facilitate, evaluate, and learn with the novices. Classroom discourse is not only constrained by teachers' professional disposition but is also by conceptions, perceptions, beliefs, ideologies, and attitudes that enumerate a culture of a people (Holland, 1998). The teacher's positioning as a facilitator, a winner, a point of reference, an authority, a friend, and a co-learner in the classroom builds the student's confidence and the opportunity for grade-level rigor to be supposed (Kayi-Ayda & Miller, 2018). The triangular shapes increase tensile strength.

A mathematics learning environment is a complex conglomeration of factors, rules, interests, identities, and ideologies ranging from institutional, communal, and individual. Players in this space experience success differently and at different levels. Researchers and educators have always struggled with maximizing learning, reducing gaps in learning among learners, and creating lasting experiences for the learners. On my epic to discovering how different and similar mathematics classroom discourses can be; I converse with social constructivists; social humanists, symbolic interactionists, and ethnographers who believe that knowledge is situative and students develop it through interactions, actions, values, choices, and sharing. I have noticed that every player in the mathematics learning and doing space is tuned differently depending on their historical and current contexts, training, and belief systems. I borrow from Rubbin (2007) and Yackel & Cobb (1996) to foster a framework for my arguments and definition of a mathematics classroom. I define a mathematics classroom as a learning community with an adaptive microculture that could impede or enhance learning. The adaptation of the microculture depends on factors such as teacher in-service training, students' dynamic identities, policy reforms, institutional culture and ideology change, and individual leanings. To account for the development of students' mathematical beliefs and autonomy in a mathematical class, Yackel and Cobb (1996) presented the sociomathematical norm's framework. They relied on social constructivism, symbolic interactionism, and ethnomethodology in crafting their lenses and marking the differences between social and sociomathematical norms in a mathematics class. They believed that social and cultural processes play an integral role in students' development and sense-making of mathematical knowledge (Yackel et al., 2001). Yackel and Cobb defined sociomathematical norms as norms specific to mathematical aspects of students' interactions. They believed that the sociomathematical norms provide a lens to analyze the mathematical aspects of teachers' and students' interactions in a mathematics classroom. These sociomathematical norms are intrinsic aspects of the mathematics classroom microculture that help to analyze sophistication, efficiency, and similarities and differences in mathematical arguments. How would students develop and internalize these sociomathematical norms? How do sociomathematical norms influence mathematical classroom discourse? Yackel and Cobb (1996) provide a basis for defining and setting up productive classroom discourse; their definition of a class microculture and their underpinning of social and cultural activities in the class are in line with Holland et al. (1998) figured worlds that are central to the positioning of the students as valuable and active contributors to the classroom body of mathematical knowledge development (Gee, 1999; Rubbin, 2007). Rubbin (2007) addresses differential learning by presenting students' identities amid figured worlds and their effects on classroom discourse. Discusses the out-of-class discourses that affect the in-class discourse. I sometimes wonder how complex it is for students to discern the different discourses, to know what to carry into the class, and when to rely on which for their positioning in the class mathematical activities. I sympathize with students whose worlds are shaped and constrained by dilapidated urban neighborhoods characterized by a dense population, overstretched social amenities, underfunded schools, and a polluted environment with toxins from neighboring industries (Tate, 2008, Hogreb et al., 2012, Anderson, 2014). I wonder how this positions students from this sociocultural, political, and socioeconomic background in a mathematics classroom discourse. Rubbin's (2007) and Yackel & Cobb's (1996) articles draw from social constructivism to argue that mathematics learning occurs as a result of in-class student interactions shaped and constrained by political, socioeconomic, sociocultural, and ideological disposition within and without their learning institutions. To me, it's not okay to explicate classroom discourse and student mathematical knowledge development and sense-making without exploring such factors. Holland et al. (1998) argue that these factors constitute the figured worlds. They dictate the teachers' and students' identities, values, and actions they embody in any mathematical classroom. I am therefore bothered by how figured worlds impact mathematical classroom discourse. Join me as I try to build knowledge around these research questions: i) To what extent do students' out-of-class experiences affect their in-classroom interactions? and ii) To what extent do target training and math coaching improve in-service mathematics teachers' pedagogical content knowledge and figured identities, and how does this impact their mathematics classroom discourse pedagogy? References Gee, J. P. (1999). Mind and Society: A Response to Derek Edwards’‘Emotion Discourse’. Culture & Psychology, 5(3), 305-312. Hogrebe, M. C., & Tate IV, W. F. (2012). Geospatial perspective: Toward a visual political literacy project in education, health, and human services. Review of Research in Education, 36(1), 67-94. Holland D., Lachicotte W., Skinner D., & Cain C. (1998). Identity and agency in cultural worlds. Cambridge, MA: Harvard University Press. Rousseau Anderson, C. (2014). Place Matters: Mathematics Education Reform in Urban Schools. Journal of Urban Mathematics Education, 7(1), 7-18. Rubin, B. C. (2007). Learner identity amid figured worlds: Constructing (in) competence at an urban high school. The Urban Review, 39(2), 217-249. Tate, W. F. (2008). Putting the" Urban" in mathematics education scholarship. Journal of Urban Mathematics Education, 1(1), 5-9. Yackel, E., & Cobb, P. (1996). Sociomathematical norms, argumentation, and autonomy in mathematics. Journal for research in mathematics education, 27(4), 458-477. Yackel, E. (2001). Explanation, Justification, and Argumentation in Mathematics Classrooms. My journey to discover; is preceded and trailed by geospatial factors.

Today I was reflecting on my past life experiences and my interactions with people at different stages of life among varied communities; I noticed that every activity is governed by some salient rules that are non-negotiable. These largely depend on the belief systems and underlying ideologies of such communities. These rules fashion out the social patterns and cultural practices of the community. They act as rating scales for what is acceptable or not acceptable; Shabtay and Heyd-Metzuyanim (2019) refer to these as figured identities. I have attempted to view this in the humanistic approaches to mathematics learning lens to center my mathematics classroom in a community woven by social practices, cultural beliefs, and ideological perspectives. I concur with Yackel & Cobb (1996) and Yackel et al. (2001) that we cannot separate an individual's thinking and sense-making from their social experiences, culture, and ideology. It spells out individuals' identities. I would therefore imagine the diversity in identity students and teachers bring to mathematics classrooms. As a teacher, one should account for the various figured identities presented in their classes. The teacher should therefore be well equipped with pedagogical content knowledge, content knowledge, and discourse pedagogy knowledge (Shulman, 1986) to position them as agents of facilitating math thinking and sense-making. My challenge is to establish how students' and teachers' figured identities impact classroom discourse. I trail the humanists, social constructivists, symbolic interactionists, and ethnomethodologists to fetch, frame, and define a reflective math classroom discourse. To quantify the effects of figured identities on classroom discourse, I would explore teachers' in-moment moves, professional noticing, valuing student strategies, and organizing and orchestrating classroom discourse. I would also evaluate differences in these traits between classes facilitated by deliberately in-service trained and non-trained teachers as they try to overcome the effects of geospatial factors in orchestrating classroom discourse. How far any player in this field goes would be determined by the social engagement rules, community beliefs, culture, and ideologies besides the geographical landscape.

Most folks around the USA live in age-long, dilapidated urban neighborhoods characterized by a dense population, overstretched social amenities, underfunded schools, and a polluted environment with toxins from neighboring industries (Tate, 2008, Hogreb et al., 2012, Anderson, 2014). Tate and Hogreb et al. observe that students from these neighborhoods have shown diminishing performance in pre-K-12 algebra. Masingila (1993) observed that students' out-of-class experiences are integral to their in-class learning processes, a notion shared by Gravemeijer (1994) as he explores Realistic Mathematics Education. I concur with Tate (2008) that geospatial factors contribute a large percentage of what students carry to the mathematics classroom or their lived knowledge of the objects of learning. I center my study on mathematics classroom discourse, leveraging social justice-based mathematics training for in-service and pre-service teachers, enriched learning resources, and triple-strand community engagement to improve students' experiences necessary to spur constructive mathematics classroom discourse.

My training as a STEM teacher majoring in Mathematics Education prepared me for a lifetime dream of becoming a math educator and part of the solution to the challenges learners face in learning and doing mathematics. I owe it to my elementary school mathematics teacher, who undoubtedly changed my view of mathematics in my formative years. I have taught mathematics for over ten years, interacted with students at different levels, trained in-service, and pre-service teachers worked with faculty members in research projects at Syracuse University and noticed pedagogical gaps resulting from either math content mastery or teaching strategy. I hold a belief that excellent math content mastery, as well as excellent math teachers, are central to teaching and learning mathematics. I desire to develop in-depth knowledge and skills of research and quality math instruction and impart these to future teachers. My goal is to be part of the team which would reengineer the classroom environment, the teaching tools, and design theoretical frameworks through research to influence the policymakers and the practitioners in the struggle for equal opportunity for all students in the math learning space. For these and other reasons, I chose to pursue a career as a mathematics educator, aspiring to be a college professor specializing in mathematics education and research in progressive pedagogies that would support social justice, equity, and inclusion in the broad mathematics learning space. Wild goose family wining over geospatial factors to bring up its chicks, the teachers in this family lead from both ends, experience the environment together with the chicks! I feel learning mathematics should be such experiential and provide opportunity for both the teacher and the student to have a learning exploration through reflective dialogues.

The long weekend is gone! I have to revisit where we left it with professor Rebecca Rogers. In her book Critical Discourse Analysis in Education, she uses Gee's lens to map out the learning construct by elucidating the components of Discourse. We referred to Gee (1996) and concurred that social interaction patterns, personal identity, and sharing of experiences are what constitutes a discourse. Several factors permeate social interaction patterns; math teachers' figured identity (Shabtay & Heyd-Metzuyanim, 2019), students' background, language disposition, institutional culture, ethnicity, and race. An individual personal character would also play a role in advancing math classroom discourse; for instance, introverts tend to share less compared to extroverts. I limit my sight to those experiences in or out of the classroom that qualifies and relates to mathematics. Masingila (1993) believes that students' everyday situation experiences are just as valuable as the conventional mathematics curriculum. Tate (2008) asserts that students' social backgrounds, first language, ethnicity, race, and geographical residence dictate their experiences and shape their character. Such experiences are a valuable starting point in classroom discourse. As math teachers, we will always have the challenge of how to make students' in-class discourse count. Most of the time, converting the students' out-of-class experiences and relating them to conventional math curricula is a daunting task. To facilitate productive math classroom social interactions; the teacher should be well informed about the students' text inference, social context, culture, and institutional values (Gee, 1999). Let me drop it here for now. Next, I will be listening to James Gee and Fairclough in a bid to understand the differences between Discourse and discourse. Focusing my Lenses to Understand the Terrain.

We may not discuss or imagine our children's mathematics learning and doing devoid of thoughts about geospatial factors. Tate (2008) observed that geospatial factors contribute a large percentage of what students carry to the mathematics classroom or their lived knowledge of the mathematics objects of learning. Geospatial factors in this context represent the space and place where students and teachers of mathematics reside. Space represents the environmental factors, socioeconomic factors, political factors, culture, language, or ethnicity, while place represents the geographical location (urban or suburban). Join me in my upcoming posts as I unpack research findings on social justice in mathematics education.