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We describe mathematics classroom teaching practice in an urban Canadian prairie Cree-bilingual school using the term "Cree mathematizing," which, to us, means (re)considering Euro-Western school mathematics from the perspectives of the Cree people engaging with the content. "Cree mathematizing" takes the form of classroom lessons in which mathematical terms are translated between English and Cree, shared through stories situated in time, place, and relationships, and contextualized by the experiences of the students and teachers. In terms of the narrative conception of identity-making, "Cree mathematizing" is a process of engaging in school mathematics that necessitates Cree educators and students to understand themselves as producing mathematics through their unique experiences and stories, making "Cree mathematizing" a partial representation of identity. We argue that "Cree mathematizing" is a subversive practice that challenges the ways Euro-Western school mathematics is taught as a culture-free, apolitical, and decontextualized endeavour that is devoid of human narratives of experience.

In North American mathematics education, many practitioners highlight a disparity in achievement between Indigenous and non-Indigenous students, and claim that incorporating Indigenous perspectives in mathematics provides a more inclusive teaching approach. However, our analysis shows that there is a stream of North American practitioners who do not use anti-oppressive or decolonizing discourses, including those who claim to be motivated by social justice education. By avoiding or not emphasizing colonization, ongoing racism, and oppression in Indigenous mathematics education, these practitioners are perpetuating a false sense of the origins of inequality. Furthermore, the quest for Indigenous cultural connections in mathematics sometimes has consequences such as placing blame on Indigenous peoples for not being authorities on their cultures, perpetuating stereotypes, homogenizing Indigenous cultures while reducing their history and knowledge to superficial artifacts, and preserving a sense of the inferiority of Indigenous peoples when it comes to understanding and learning mathematics.

Ninety-seven education students majoring or minoring in mathematics had their math homework examined in a Number Theory or Abstract Algebra course. Each student's homework was observed for the purpose of identifying common errors and misconceptions when writing mathematical proofs. The results showed that students collectively made four recurring errors: assuming the conclusion in order to prove the conclusion, proving general statements using specific examples, not proving both conditions in a biconditional statement, and misusing definitions. In the same courses taken subsequently by 91 new students, we informed them about these common errors prior to assigning their homework to see how the students' proving processes would differ. The results showed that more exercises were left blank with comments such as "I'm not sure how to start the proof", and that many students provided unnecessary examples to supplement their valid proofs.

Dans l'enseignement des mathematiques en Amerique du Nord, bon nombre de praticiens soulignent l'existence d'une disparite entre les eleves autochtones et non autochtones quant aux resultats scolaires et soutiennent que l'incorporation des points de vue autochtones dans les mathematiques donne lieu a une approche pedagogique plus inclusive. Notre analyse montre toutefois qu'une kyrielle de praticiens nord-americains n'ont pas recours a des discours anti-oppressifs ou de decolonisation, notamment ceux qui se disent motives par l'education a la justice sociale. En evitant ou en ne mettant pas en evidence la colonisation, le racisme persistant et l'oppression dans l'enseignement des mathematiques aux autochtones, ces praticiens perpetuent une fausse impression sur les origines de l'inegalite. En outre, la quete de liens culturels autochtones en mathematiques entraine parfois comme consequence, d'une part, le rejet du blame sur les peuples autochtones dont le manque d'autorite vis-a-vis de leurs cultures aurait eu pour effet de perpetuer des stereotypes et d'homogeneiser les cultures autochtones tout en reduisant leur histoire et leurs savoirs a des artefacts artificiels et, d'autre part, la perpetuation d'un sentiment d'inferiorite chez les peuples autochtones quant a la comprehension et a l'apprentissage des mathematiques. Mots-cles : enseignement des mathematiques, decolonisation, education autochtone, antiracisme, education anti-oppressive, colonisation, formation a l'enseignement In North American mathematics education, many practitioners highlight a disparity in achievement between Indigenous and non-Indigenous students, and claim that incorporating Indigenous perspectives in mathematics provides a more inclusive teaching approach. However, our analysis shows that there is a stream of North American practitioners who do not use anti-oppressive or decolonizing discourses, including those who claim to be motivated by social justice education. By avoiding or not emphasizing colonization, ongoing racism, and oppression in Indigenous mathematics education, these practitioners are perpetuating a false sense of the origins of inequality. Furthermore, the quest for Indigenous cultural connections in mathematics sometimes has consequences such as placing blame on Indigenous peoples for not being authorities on their cultures, perpetuating stereotypes, homogenizing Indigenous cultures while reducing their history and knowledge to superficial artifacts, and preserving a sense of the inferiority of Indigenous peoples when it comes to understanding and learning mathematics. Keywords: mathematics education, decolonization, Aboriginal education, anti- racism, anti-oppressive education, colonization, teacher education, Indigenous education, Miscalculations: Decolonizing and Anti-Oppressive Discourses in Indigenous Mathematics Education Introduction Mathematics education is a broad area of research and practice that looks at topics ranging from the cognitive psychology of [...]

A statistical model for ultrawideband (UWB) off-body communication channels is proposed. The presented results are the outcome of extensive real-body measurements carried out in the frequency range between 3.5 and 6.5 GHz in typical indoor environments. The signal power gain is modeled by a log-linear dual-breakpoint model, the parameters of which depend on both the body orientation as well as the distance between the transmitter and the on-body sensor. The general trend implies that in large distances, the received signal strength is less sensitive to changes in the body orientation angle, especially if propagation occurs in dense multipath environments. Furthermore, the small-scale channel variations of the total received signal strength are found to follow a normal distribution. This fact was verified by means of the central limit theorem (CLT), since correlation between multipath components is found to be negligible. Moreover, time dispersion analysis is provided by means of RMS delay spread. Finally, based on the newly estimated parameters, a model implementation for wideband power is proposed and several comparisons between the empirical data and the simulation results are presented. Index Terms--Body to access point (BAP) channel, total power gain, ultrawideband (UWB), wireless body area networks (WBAN).

Two new models used to characterize polarization diversity at the mobile are presented and discussed. The first model is built upon existing theoretical models at a base station to demonstrate how those principles apply to the mobile fading environment. Due to limitations of antennas at the mobile, this extended model, although relevant, is not sufficient to characterize polarization diversity of the antennas; therefore, this paper moves on to show how a new approach to polarization diversity at the mobile exists as an inherent feature within an angular diversity system. Results show that, for two polarizations in a fading environment, the best overall output occurs with a [+ or -] 4-45[degree] element configuration, although the diversity combiner itself has optimum performance with a [+ or -] 67.5[degree] configuration due to lower correlation at the input. The second model is also used to demonstrate how differently polarized dipoles are using polarization diversity inherent within an angular diversity system. Index Terms--Antenna diversity, branch difference, correlation, cross-polar ratio, efficiency loss.