{"id":498,"date":"2017-12-03T22:43:41","date_gmt":"2017-12-04T06:43:41","guid":{"rendered":"https:\/\/blogs.ubc.ca\/danabjornson\/?p=498"},"modified":"2018-03-11T12:29:18","modified_gmt":"2018-03-11T19:29:18","slug":"the-non-oppressive-mathematics-classroom-a-comprehensive-guide-towards-creating-a-third-space","status":"publish","type":"post","link":"https:\/\/blogs.ubc.ca\/danabjornson\/2017\/12\/03\/the-non-oppressive-mathematics-classroom-a-comprehensive-guide-towards-creating-a-third-space\/","title":{"rendered":"The Non-Oppressive Mathematics Classroom:  A Comprehensive Guide Towards Creating a Third Space"},"content":{"rendered":"<blockquote>\n<p class=\"Title2\" style=\"text-align: center;\"><span lang=\"EN-US\">ETEC 521: Indigeneity, Technology, and Education<\/span><\/p>\n<p class=\"Title2\" style=\"text-align: center;\"><span lang=\"EN-US\">Professor: Dr. Michael Marker<\/span><\/p>\n<p class=\"Title2\" style=\"text-align: center;\"><span lang=\"EN-US\">December 3, 2017<\/span><\/p>\n<\/blockquote>\n<h5 style=\"text-align: center;\">Abstract<\/h5>\n<p>Perhaps the most commonly pondered question from frustrated mathematics students, across grades and cultures, is \u201cWhen am I ever going to use this?\u201d \u00a0For exasperated fifteen-year-old Indigenous learners, this question transcends feelings of frustration; it clashes with their entire worldview. Traditionally, mathematics has been taught entirely from a Western perspective, a mindset that is firmly rooted within the pedagogy of oppression. This essay begins to address <em>why<\/em> mathematics educators need to take a step back from strictly traditional approaches, <em>how<\/em> this shift can occur within Western high school mathematics curriculum, and <em>how<\/em> Indigenous and non-Indigenous students can mathematically thrive within a culturally inclusive, third space.<\/p>\n<p style=\"text-align: center;\"><em>Keywords<\/em>:\u00a0 Indigenous, non-Indigenous, mathematics, non-oppressive, worldviews, third space, high school<\/p>\n<p>&nbsp;<\/p>\n<h5 style=\"text-align: center;\">Protocols of Place<\/h5>\n<p>I would like to acknowledge that this essay was written on the traditional territory of the Lkwungen people.\u00a0 I would like to further acknowledge the Songhees First Nation and the Esquimalt First Nation on whose territory I live, I learn, and I work. For the purpose of situating myself within this research essay, I am a high school mathematics and physics teacher, of White settler identity\u2014 adopted into a Norwegian family at birth, and, to my knowledge, originally from Italian and English heritage. I am primarily concerned with creating an inclusive, non-oppressive learning environment for my students, reducing the effects of anxiety in the classroom, and maintaining the academic rigor required for courses in senior mathematics and physics.<\/p>\n<h3 style=\"text-align: center;\">Introduction<\/h3>\n<p>Class begins promptly at 12:20 P. M., and the agenda is on the board:<\/p>\n<ol>\n<li>Homework Questions?<\/li>\n<li>Hand-in homework.<\/li>\n<li>New section: Polynomial expansions.<\/li>\n<\/ol>\n<p>Today, nobody has any questions from last night\u2019s work.\u00a0 The teacher is pleased with herself as she thinks that she must have been very effective the class before; however, this thought passes quickly, as fewer than half of her students proceed to hand in the work. She continues to teach the new lesson, as <em>she<\/em> was taught when she was in Mathematics 10.\u00a0 She provides notes; students write the notes; students practice, and repeat. Her degree in mathematics has served her well\u2014she knows what qualities the students need to succeed and to be \u201cefficient\u201d with their processes, as these were the qualities that she required.\u00a0 If you were to ask her if she thought that she was contributing to an oppressive learning environment, she would not hesitate to say, \u201cAbsolutely not.\u201d<\/p>\n<h3 style=\"text-align: center;\">The Oppressive Math Classroom<\/h3>\n<p>For those of us who were in high school before 2000, it is almost guaranteed that we were taught math in what is commonly called a \u201ctraditional\u201d format, as described in the introduction. Our teachers gave notes; we wrote notes; we practiced, and were assessed. Consequently, many of us who see ourselves in the role of \u201cmath teacher\u201d continue to teach in this traditional format. At first consideration, it may appear to be unwarranted, even outrageous, to say that learning in a traditional environment is \u201coppressive.\u201d<\/p>\n<p>In its most extreme form, \u201ctraditional mathematics education\u201d can easily be equated with \u201cmath indoctrination.\u201d \u00a0A teacher who prescribes mathematics indoctrination will provide one-sided arguments, attempt to erase learners\u2019 differences from their processes, employ language that would pit vice against virtue, and could claim a right versus wrong way of problem-solving (Nodoushan &amp; Pashapour, 2016). \u00a0Students in these classrooms must follow the \u201coptimal way,\u201d be efficient with their time, and be precise and deliberate with their strategy (Russell &amp; Chernoff, 2012). Assessments are typically timed and performed individually, so that fully indoctrinated students will likely be successful; those who do not learn in this way risk failure, as technically this constitutes an oppressive learning environment.<\/p>\n<p>In his most influential work, <em>Pedagogy of the Oppressed<\/em>, Paulo Freire describes mainstream education with the metaphor \u201cthe banking concept of education.\u201d Although he wrote this work in 1968, it is common to find educators today possessing attitudes and following practices that imply that the teacher\u2019s role is to merely deposit information into students as though they were receptacles. Other oppressive practices and attitudes that Freire lists include these:<\/p>\n<ul>\n<li>The teacher knows everything, and the students know nothing.<\/li>\n<li>The teacher talks, and the students listen\u2014meekly.<\/li>\n<li>The teacher acts and the students have the illusion of acting through the action of the teacher.<\/li>\n<li>The teacher chooses the program content, and the students (who were not consulted) adapt to it. (p. 73, Freire)<\/li>\n<\/ul>\n<p>Studies have revealed that students are less motivated in classrooms where the teacher is overly controlling, where they have fewer options for academic study, and have fewer opportunities to voice their opinions (Preston &amp; Claypool, 2013). Should mathematics educators wish to evolve towards a non-oppressive practice, they must be prepared to loosen their academic leashes.<\/p>\n<p>Also drawing from Freire\u2019s work, Dr. Kevin Kumashiro (<a href=\"http:\/\/www.kevinkumashiro.com\/\">www.kevinkumashiro.com<\/a>) has devoted his life to anti-oppressive education, amongst other forms of equalization in the classroom. Kumashiro argues that anti-oppressive teaching practices are routinely resisted when they do not fall in line with the entrenched ideations of what education is \u201csupposed\u201d to be. \u00a0Compacting this resistance is that, despite the good intentions of anti-oppressive sympathizers, teachers will often contribute to oppression unknowingly within their classrooms. As oppressive practices are not always identified, they may be repeated over and over, and thus <em>experienced<\/em> over and over, a cycle which results in students\u2019 believing that there are only certain acceptable forms of identifying or thinking (Kumashiro, 2002).<\/p>\n<p>On the other hand, some reformists are not simply looking at what <em>is<\/em> being done in the math classroom; rather, they are focusing on what is <em>not<\/em> being done. Stavrou and Miller maintain that, although there are many educators that recognize the disparity between Indigenous and non-Indigenous learners, there is a disconnect between what is espoused to be decolonizing, anti-oppression mathematics education and the discourse itself produced by those scholars in the field of these topics. \u00a0Often, anti-oppressive \u201cwell-meaners\u201d will fall short in their attempts to provide decolonized education. Although they promote cultural understanding and non-Western mindsets, they neglect to address and to challenge the root causes of oppression, namely how inequalities are entrenched within our schools, and how to counter Western knowledge as superior to Indigenous ways of knowing. They also warn about the harmful effects of providing \u201cculturally relevant mathematics\u201d that is superficial in nature, such as teaching circular geometry by showing a medicine wheel. In circumstances where Indigenous knowledge is utilized devoid of context and meaning, not only can its use propagate stereotypes, educators risk the homogenization of Indigenous cultures and knowledge (Stavrou and Miller, 2017). \u00a0Also at risk, when simplistic versions of culturally responsive teaching are at play, is that the cultural homogenization can lead to increased instances of \u201cothering\u201d the non-dominant culture (Keddie, Gowlett, Mills, Monk, &amp; Renshaw, 2012). Ultimately, practices that reinforce divisions of \u201cus and them\u201d are oppressive and obstructive in the creation of a safe learning environment for all. Moreover, it is critical that teachers not trivialize or decontextualize Indigenous knowledge if the learning needs of Indigenous students are to be truly valued.<\/p>\n<h3 style=\"text-align: center;\">Creating a Third Space<\/h3>\n<p>When two cultures combine and co-evolve in such a way that neither is placed as the dominant culture, but more as a <em>new <\/em>culture, some scholars describe this synthesis as representing the third space (Lipka, Sharp, Adams, &amp; Sharp, 2007). Should there be a third space in a mathematics classroom, the new culture would have the potential to challenge existing hegemonic systems, and provide space for addressing racism and oppression, thereby creating a nurturing learning environment for all. \u00a0For the classroom to represent a third space authentically, educators must learn about the roots of oppression, such as colonization (past and present), residential schools, and racism (Stavrou &amp; Miller, 2017).\u00a0 These topics require educators to situate themselves for prolonged periods of time; considerably more time than an afternoon of Professional Development! Should teachers understand the roots of Indigenous oppression (as obvious as this will sound), non-Indigenous educators must then learn about Indigenous worldviews that can be embedded into their classroom\u2019s third space.<\/p>\n<h4>Indigenous Worldviews in the Mathematics Classroom<\/h4>\n<p>Academic mathematics educators have many \u201creasons\u201d to not embrace Indigenous worldviews within their classrooms.\u00a0 These may include restrictions in teaching time, having too many learning outcomes to address, not understanding Indigenous culture or worldviews, and\/or not valuing Indigenous worldviews for their subject matter.<\/p>\n<p>Long before Lev Vygotsky developed his socio-cultural learning theory that focuses on the critical nature of More Knowledgeable Others (MKOs), Indigenous cultures were harnessing the wisdom of their own MKOs, namely, their elders.\u00a0 Vygotskian Theory relies on MKOs to help learners flourish within their Zone of Proximal Development.\u00a0 This is the space where a learner can be successful, not on their own, but with support from someone with more knowledge (John-Steiner &amp; Mahn,1996). Elders in Indigenous communities are not only experts within their fields; they also act as conduits of culture, language, and history. Where successful examples of decolonized education have been documented, knowledge from elders is part of authentic, contextualized mathematical learning, that is far from being trivial (Lipka <em>et al<\/em>, 2007; Kawagley &amp; Barnhardt, 1998 Preston &amp; Claypool, 2013; Munroe, Lunney Borden, Murray Orr, Toney, &amp; Meder, 2013).\u00a0 A beautiful example of the sharing of an elder\u2019s wisdom recently came my way on my Facebook feed. <a href=\"https:\/\/www.facebook.com\/margaret.neketa\/posts\/1640262779327006?pnref=story\" target=\"_blank\" rel=\"noopener\">It was a video of a young girl<\/a>, not more than six years old, deboning a salmon with a rather large blade.\u00a0 Her mother, Margaret Neketa, was behind the camera providing encouragement, not stepping in to help physically, and allowing her daughter to make her own mistakes. At one point, the girl did make an error, and the mother calmly told her it was \u201cokay to make mistakes\u201d; consequently, the girl continued with even more confidence (Neketa, M., 2017). Although the little girl\u2019s accomplishment was commendable, the magnitude of this mother\u2019s gift of empowerment and practical, hands-on knowledge, is unmeasurable. Furthermore, how can a non-Indigenous, high school mathematics teacher draw lessons from this example of non-oppressive education?<\/p>\n<p>Although academic mathematics is not traditionally \u201chands-on,\u201d there are occasional opportunities that lend themselves to direct, practical experience.\u00a0 Consider these examples:<\/p>\n<ol>\n<li>Surface Area: creating three-dimensional models from net diagrams.<\/li>\n<li>Trigonometry: using a clinometer to determine inaccessible heights.<\/li>\n<li>Relations and Functions: collecting actual data to graph, as opposed to using premade, tables of values.<\/li>\n<li>Domain and Range, Linear\/Quadratic Equations, Inequalities: recreating artwork on a coordinate plane using the free, online Desmos platform (<a href=\"https:\/\/docs.google.com\/presentation\/d\/1vCA-2i3F_C3VPZFolWg2lvMZWo4tg8Kp74ojcyCYFu0\/edit?usp=sharing\">example<\/a> of student work).<\/li>\n<\/ol>\n<p>Although the time constraints and the number of learning outcomes to be mastered are not within an educator\u2019s locus of control, I have found that, in my own practice, it is manageable to utilize a few practical applications within each semester. I would also reinforce the premise that to non-trivialize or decontextualize Indigenous ways of knowing, the activities should not \u201cforce\u201d Indigeneity into the process. However, providing students with choice, such as the piece of artwork to be used in their Desmos activity, is the key because students may choose the artwork that has meaning to them. \u00a0Additionally, it is important to avoid micro-managing approaches as the students are working.\u00a0 Allowing them to decide how and when they need help licenses students to have control over their learning process.\u00a0 In relinquishing centralized control, educators are shifting the authority structure in their classroom, while still maintaining classroom management and the quality of the lesson content (Lipka, <em>et al,<\/em> 2007). \u00a0I do not believe that hands-on activities are possible for every lesson in academic mathematics, however, if we can occasionally weave practical applications throughout appropriate units, the result situates the learning in a non-oppressive, third space.<\/p>\n<p><strong>Collaboration with peer MKOs.<\/strong> Learning together via collaborative techniques is another Indigenous worldview that lends itself to mathematics in numerous ways. Vygotsky believed that MKOs could be found from all ages, not just authority figures (John-Steiner &amp; Mahn, 1996).\u00a0 In my online, ETEC 521 graduate course (Indigeneity, Technology, and Education), I watched an interview with Dr. Lee Brown, a leading expert in emotional education and creating healthy learning environments for Aboriginal learners. Here, he describes how Western culture historically promotes individualistic learning practices, whereas Indigenous cultures believe that one learns more effectively collectively.\u00a0 He also maintains that, when Western classrooms fail to reflect Indigenous values, educators risk having their Indigenous students leave their classroom. What, then, can the academic mathematics teacher do both to reduce that risk and to draw from Indigenous wisdom that endorses the interconnectedness of shared knowledge?<\/p>\n<p><em>Peer instruction.<\/em> Harvard physics professor Eric Mazur is known for his alternative instructional style called peer instruction (PI). \u00a0PI is a technique in which lessons do not contain direct instruction, as the instructor\u2019s expectation is that students will pre-read, prior to the meeting time.\u00a0 Instead of direct instruction, classes include qualitative, multiple-choice questions that students vote on individually, discuss responses amongst each other, and then revote individually. The instructor moderates a class discussion that is responsive to the final voting results. Mazur explains that the success in PI is the result students\u2019 being able to explain concepts more effectively than an experienced instructor for each other. As the peer-MKOs have only just learned the material, they have an easier time explaining from a perspective that the confused learner can more easily digest (Serious Science, 2014).<\/p>\n<p>I have used a modified version of PI in my high school classroom for almost twenty years. Although I still deliver content traditionally in the form of notes, I have students discuss answers with each other throughout the lesson. Subsequently, my lessons can be noisy yet also vibrant because all students have opportunities to share their thought-processes daily. When we review material, I incorporate voting questions as directed by Mazur\u2019s PI methodology.<\/p>\n<p><em>Formative collaborative review.<\/em> Tabletop whiteboards allow regular, small-scale review to be done collaboratively, then shown to me from across the room.\u00a0 As students arrive at correct answers on their whiteboards, <em>they<\/em> become MKOs to pairs that are having difficulties.\u00a0 \u201cSnowball Math\u201d is another technique in which students are on teams, armed with review questions that they wrote onto paper \u201csnowballs.\u201d For two minutes, snowballs are hurled across the room, and teams then must collaboratively solve any snowballs that were left in their zone. I just recently found this activity in a resource called the \u201c<a href=\"http:\/\/www.fnesc.ca\/resources\/math-first-peoples\/\">Math First Peoples Resource Guide<\/a>\u201d (p. 22), produced by the First Nations Education Steering Committee in British Columbia. Within this guide, there is a multitude of ideas that foster third space creation.<\/p>\n<p><em>Collaborative assessments.<\/em> Mathematical assessment provides another opportunity to utilize collaborative, third space affordances. Quizzing done in a collaborative format, provides students with formative assessment, that reduces \u201ctest stress\u201d amongst anxious mathematics learners. Allowing students the freedom to assess alone or in pairs, closed- or open-book, creates academic choice that caters to the individual needs of students. Marking their own work again shifts the responsibility towards the students, who can then obtain credit for handing in corrected work, should educators wish to record assessments.\u00a0 Unit tests may also be done in a collaborative format, utilizing what is known as two-stage testing. During two-stage collaborative testing, students complete a shortened regular test individually, then in groups of four they complete the same test collaboratively.\u00a0 Educators blend the two marks, say with an 80%-20% split. Students report understanding the material better, having decreased anxiety, and feeling a heightened sense of community within the class; whereas educators report higher attendance rates, lower rates of course dropouts and higher final grades (Knierim, Turner, &amp; Davis, 2015).<\/p>\n<p>As opposed to subjecting our students to repetitive forms of hegemonic oppression, these collaborative techniques repeatedly reinforce Dr. Brown\u2019s mantra \u201cTogether, we are stronger.\u201d\u00a0 Moreover, collaborative learning practices shift the power to the students and away from the authority figure, thereby situating the learning in the third space.<\/p>\n<p><strong>Honouring multiples ways of knowing. <\/strong>Most high school mathematics educators have considerable experience in their field at the postsecondary level, and subsequently have an informed opinion as to how mathematical processes should optimally be done.\u00a0 Optimization of process, however, is yet another practice that may be oppressive in the eyes of our students. Russell and Chernoff (2012) strike at the heart of this issue by saying, \u201cAs Indigenous students continue to struggle with mathematics teaching and learning they are concurrently struggling with yet one more aspect of this assimilation, and, thus, we are causing harm through this unethical process\u201d (p. 116). \u00a0\u00a0Traditionalists will undoubtedly take offence to the assertion that their pedagogical style is \u201cunethical.\u201d What is of greater concern to me, however, is that by teaching students that there is an optimal method that differs from their method, repeatedly sends the message that the students\u2019 way of knowing is not valued. For those students who already have deep-seeded feelings of being devalued in broader contexts, rejecting their mathematical thinking may in turn perpetuate the perception that their Indigenous ways of knowing are also not valued; hence they themselves may perceive that they are not valued in our classrooms.<\/p>\n<p>When multiple methodologies, in combination with cultural relevance, are presented in mathematics, students\u2019 motivation and engagement with the mathematics increases (Kisker <em>et al<\/em>, 2011). Admittedly, in academic, high school mathematics courses, situating the mathematics within a cultural context is extremely difficult, as the mathematics is vastly learned, to perform higher levels of mathematics. Providing multiple methodologies and celebrating all forms of solutions are entirely possible in academic mathematics, however. \u00a0Expanding binomial factors, for example, can be done in a variety of ways (<em>Table 1<\/em>).<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-499 aligncenter\" src=\"https:\/\/blogs.ubc.ca\/danabjornson\/files\/2017\/12\/table-for-project-300x242.jpg\" alt=\"\" width=\"305\" height=\"246\" srcset=\"https:\/\/blogs.ubc.ca\/danabjornson\/files\/2017\/12\/table-for-project-300x242.jpg 300w, https:\/\/blogs.ubc.ca\/danabjornson\/files\/2017\/12\/table-for-project.jpg 650w\" sizes=\"auto, (max-width: 305px) 100vw, 305px\" \/><\/p>\n<p>Without question, my preference is to use FOIL when expanding; however, this is of little use, should higher order polynomials be involved. Therefore, I must sometimes employ an alternative strategy. Should we require this double-barreled approach for our students as well?\u00a0 In my experience, students who struggle with mathematics would prefer to learn just one strategy rather than two, so is fair to only teach to the top 50% of the class? Realistically, most students will not be taking mathematics past high school, and simply need enough academic mathematics either to graduate or possibly to enter one of countless, non-mathematics-based postsecondary programs. Moreover, it is a disservice to all our students to withhold alternative problem-solving approaches, as doing so ultimately undermines the value and creation of the third space by reinforcing a multitude of oppressive practices.<\/p>\n<h3 style=\"text-align: center;\"><strong>The Best of Both Worlds<\/strong><\/h3>\n<p>Western methodologies are not without their affordances within academic mathematics contexts, and the creation of the third space allows for those affordances to remain accessible. It is also clear to me that, when educators create a third space for their students to learn within, all students benefit from this mindful effort. Helping non-Indigenous educators engage in best-practices, the case study \u201cShe Can Bother Me, and That\u2019s Because She Cares\u201d outlines a list of universally effective teaching strategies being used with middle school students on Baffin Island, Nunavut. Some of these strategies include the following:<\/p>\n<ol>\n<li>Adapting teaching strategies to meet the needs of the students, as opposed to having students adapt to teachers\u2019 ways.<\/li>\n<li>Providing multiple learning strategies maximizes the effectiveness of students\u2019 responses.<\/li>\n<li>Providing opportunities for students to voice their own strategies produces a positive learning environment.<\/li>\n<li>Being a caring, consistent, interested, and connected teacher who neglects student deficiencies will foster student success (Lewthwaite &amp; McMillan, 2010).<\/li>\n<\/ol>\n<p>Strict, traditional Western mathematics approaches engage in few to none of these strategies, thereby requiring Indigenous students to change, and potentially devalue, their own worldview. Sadly, this conflict of worldviews may result in the isolation of Indigenous students and their marginalization from mathematics entirely (Russell &amp; Chernoff, 2012).<\/p>\n<p>Moving forward in establishing a third space in academic mathematics classrooms, educators may follow many pathways. Providing pathways that foster resilience is a focus for some, as it is a necessary quality for students to have when developing coping strategies that mitigate stressors. York University researchers have shown that increased levels of social competency resilience and heightened appreciation of cultural identity may be fostered through Aboriginal peer mentorship programs (Rawana, Sieukaran, Nguyen, &amp; Pitawanakwat, 2015). \u00a0In his paper entitled, \u201cTransforming Cultural Trauma into Resilience,\u201d Martin Brokenleg maintains that, although one can use a medicine wheel for reference, learning resilience cannot be learned from words or a poster; it must be learned through life experience. Referencing Freire\u2019s <em>Pedagogy of the Oppressed<\/em>, Brokenleg explains that, once we are convinced that we are not good enough or smart enough, the effects of oppression are internalized and very difficult to erase from our thoughts (Brokenleg, 2012). In reality, many students entering my classes at the high school level have already internalized this harmful negativity, which I often refer to as one\u2019s \u201cMath Baggage.\u201d<\/p>\n<p>As a non-Indigenous educator who is mindfully making her initial steps towards the creation of a non-oppressive, third space in her mathematics classroom, I fully recognize that, in following the pedagogy described in this essay, I have merely broken the ice in considering what needs to be an ongoing journey towards a truly non-oppressive classroom.\u00a0 Addressing the roots of oppression in a non-trivial way has not been addressed in this essay; nor was how to authentically embed contextualized mathematics within academic mathematics.\u00a0 Nonetheless, I must follow the advice that I give to my students: a person\u2019s not knowing how the entire solution plays out does not mean that he or she cannot at least <em>begin<\/em> to move towards a solution. Moreover, I must not be afraid to take risks and make mistakes in my learning, as I want my students to take risks and make their own mistakes in my classroom. Learning through life experience, honouring one\u2019s identity and one\u2019s culture, and collaboratively sharing our knowledge for the betterment of our learning community are all Indigenous worldviews that allow all students to learn at the highest levels of mathematics in a non-oppressive environment. It truly is the best of both worlds.<\/p>\n<h6>References<\/h6>\n<h6>Brokenleg, M. (2012). Transforming cultural trauma into resilience. <em>Reclaiming Children and Youth<\/em>, <em>21<\/em>(3), 9-13.<\/h6>\n<h6>First Nations Education Steering Committee. (2011). <em>Math First Peoples teacher resource guide. <\/em>Retrieved from <a href=\"http:\/\/www.fnesc.ca\/resources\/math-first-peoples\/\">http:\/\/www.fnesc.ca\/resources\/math-first-peoples\/<\/a><\/h6>\n<h6>Freire, P. (1970). <em>Pedagogy of the oppressed. <\/em>New York, NY: The Continuum International Publishing Group Inc.<\/h6>\n<h6>John-Steiner, V., &amp; Mahn, H. (1996). Sociocultural approaches to learning and development: A Vygotskian framework.\u00a0<em>Educational<\/em>\u00a0<em>Psychologist<\/em>,\u00a0<em>31<\/em>(3), 191. doi:10.1207\/s15326985ep3103&amp;4_4<\/h6>\n<h6>Kawagley, A.O., &amp; Barnhardt, R. (1998). <em>Education Indigenous to Place: Western science meets native reality. <\/em>Retrieved from <a href=\"http:\/\/www.ankn.uaf.edu\/curriculum\/Articles\/BarnhardtKawagley\/EIP.html\">http:\/\/www.ankn.uaf.edu\/curriculum\/Articles\/BarnhardtKawagley\/EIP.html<\/a><\/h6>\n<h6>Keddie, A., Gowlett, C., Mills, M., Monk, S., &amp; Renshaw, P. (2012). Beyond culturalism: Addressing issues of indigenous disadvantage through schooling.<em> The Australian Educational Researcher, 40<\/em>(1), 91-108. doi:10.1007\/s13384-012-0080-x<\/h6>\n<h6>Kisker, E. E., Lipka, J., Adams, B. L., Rickard, A., Andrew-Ihrke, D., Yanez, E. E., &amp; Millard, A. (2012). The potential of a culturally based supplemental mathematics curriculum to improve the mathematics performance of Alaska Native and other students.<em> Journal for Research in Mathematics Education, 43<\/em>(1), 75.<\/h6>\n<h6>Knierim, K., Turner, H., &amp; Davis, R. (2015). Two-stage exams improve student learning in an introductory geology course: Logistics, attendance, and grades. <em>Journal of Geoscience Education<\/em>, <em>63, <\/em>157-164. Retrieved from <a href=\"chrome-extension:\/\/oemmndcbldboiebfnladdacbdfmadadm\/http:\/nagt-jge.org\/doi\/pdf\/10.5408\/14-051.1?code=gete-site\">chrome-extension:\/\/oemmndcbldboiebfnladdacbdfmadadm\/http:\/\/nagt-jge.org\/doi\/pdf\/10.5408\/14-051.1?code=gete-site<\/a><\/h6>\n<h6>Kumashiro, K. K. (2002). Against repetition: Addressing resistance to anti-oppressive change in the practices of learning, teaching, supervising, and researching.<em> Harvard Educational Review, 72<\/em>(1), 67.<\/h6>\n<h6>Lipka, J., Sharp, N., Adams, B., &amp; Sharp, F. (2007). Creating a third space for authentic biculturalism: Examples from math in a cultural context.<em> Journal of American Indian Education, 46<\/em>(3), 94-115.<\/h6>\n<h6>Munroe, E. A., Lunney Borden, L., Murray Orr, A. Toney, D., &amp; Meader, J. (2013). Decolonizing aboriginal education in the 21st century.<em> McGill Journal of Education, 48<\/em>(2), 317-337. doi:10.7202\/1020974ar<\/h6>\n<h6><u>Munroe, E. A., Lunney Borden, L., Murray Orr, A. Toney, D., &amp; Meader, J. (2013). Decolonizing aboriginal education in the 21st century.<em> McGill Journal of Education, 48<\/em>(2), 317-337. doi:10.7202\/1020974ar <\/u><\/h6>\n<h6>Neketa, M. (2017, July 11). <em>My one and only<\/em> [Facebook post]. Retrieved from <a href=\"https:\/\/www.facebook.com\/margaret.neketa\/posts\/1640262779327006?pnref=story\">https:\/\/www.facebook.com\/margaret.neketa\/posts\/1640262779327006?pnref=story<\/a><\/h6>\n<h6>Nodoushan, M. A. S. &amp; Pashapour, A. (2016). Critical pedagogy, rituals of distinction, and true professionalism.<em> I-Manager&#8217;s Journal of Educational Technology, 13<\/em>(1), 20.<\/h6>\n<h6>Preston, J. P., &amp; Claypool, T. R. (2013). Motivators of educational success: Perceptions of Grade 12 Aboriginal students. <em>Canadian Journal of Education.<\/em> <em>36<\/em>(4), 257-279.<\/h6>\n<h6>Rawana, J. S., Sieukaran, D. D., Nguyen, H. T., &amp; Pitawanakwat, R. (2015). Development and evaluation of a peer mentorship program for aboriginal university students. <em>Canadian Journal of Education. 38<\/em>(2), 1-34.<\/h6>\n<h6>Russell, G. L., &amp; Chernoff, E. J. (2013). The marginalisation of indigenous students within school mathematics and the math wars: Seeking resolutions within ethical spaces.<em> Mathematics Education Research Journal, 25<\/em>(1), 109-127. doi:10.1007\/s13394-012-0064-1<\/h6>\n<h6>Serious Science. (2014, June 18). <em>Peer Instruction for Active Learning &#8211; Eric Mazur<\/em> [Video file]. Retrieved from <a href=\"https:\/\/www.youtube.com\/watch?v=Z9orbxoRofI\">https:\/\/www.youtube.com\/watch?v=Z9orbxoRofI<\/a><\/h6>\n<h6>Stavrou, S. G., &amp; Miller, D. (2017). Miscalculations: Decolonizing and anti-oppressive discourses in indigenous mathematics education.<em> Canadian Journal of Education, 40<\/em>(3), 92-122.<\/h6>\n","protected":false},"excerpt":{"rendered":"<p>ETEC 521: Indigeneity, Technology, and Education Professor: Dr. Michael Marker December 3, 2017 Abstract Perhaps the most commonly pondered question from frustrated mathematics students, across grades and cultures, is \u201cWhen am I ever going to use this?\u201d \u00a0For exasperated fifteen-year-old &hellip; <a href=\"https:\/\/blogs.ubc.ca\/danabjornson\/2017\/12\/03\/the-non-oppressive-mathematics-classroom-a-comprehensive-guide-towards-creating-a-third-space\/\">Continue reading <span class=\"meta-nav\">&rarr;<\/span><\/a><\/p>\n","protected":false},"author":38898,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3242,2721,524,5700,370725,58021],"tags":[],"class_list":["post-498","post","type-post","status-publish","format-standard","hentry","category-assessment","category-collaboration","category-etec-521","category-indigenous-culture","category-peer-instruction","category-vygotsky"],"_links":{"self":[{"href":"https:\/\/blogs.ubc.ca\/danabjornson\/wp-json\/wp\/v2\/posts\/498","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/blogs.ubc.ca\/danabjornson\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blogs.ubc.ca\/danabjornson\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blogs.ubc.ca\/danabjornson\/wp-json\/wp\/v2\/users\/38898"}],"replies":[{"embeddable":true,"href":"https:\/\/blogs.ubc.ca\/danabjornson\/wp-json\/wp\/v2\/comments?post=498"}],"version-history":[{"count":3,"href":"https:\/\/blogs.ubc.ca\/danabjornson\/wp-json\/wp\/v2\/posts\/498\/revisions"}],"predecessor-version":[{"id":594,"href":"https:\/\/blogs.ubc.ca\/danabjornson\/wp-json\/wp\/v2\/posts\/498\/revisions\/594"}],"wp:attachment":[{"href":"https:\/\/blogs.ubc.ca\/danabjornson\/wp-json\/wp\/v2\/media?parent=498"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blogs.ubc.ca\/danabjornson\/wp-json\/wp\/v2\/categories?post=498"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blogs.ubc.ca\/danabjornson\/wp-json\/wp\/v2\/tags?post=498"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}