Indigenous Mathematizing
Indigenous languages are verbbased, whereas Western languages are nounbased. This fundamental difference in cultural world views is respected by the use of the term “mathematizing” (a verb). It is exemplified by activities in which counting, measuring, locating, designing, playing, or explaining quantitatively occur within an Indigenous culture.
It is imperative that teachers understand Indigenous lesson plans must be considered holistically. That means that the Indigenous teachings and intentions that are part of the language and culture must be considered. NonIndigenous teachers should consider consulting Indigenous advisors to ensure that the integrity of the content is not unintentionally lost or compromised.
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Synopsis 
Curricular Connection 
Indigenous Mathematizing and Ways of Knowing 
Freestyle Looming and Probability^{1}Krysta Shemrock 

FM30.4 Extend understanding of odds and probability.FM30.5 Extend understanding of the probability of two or more events. Probability trees. 
Before contact with Europeans, wampum belts were designed to record stories and events, especially treaty relationships; and They were loomed using natural materials (e.g., porcupine quills, seashells, deer antlers). 
Picario:^{2} A Traditional Indigenous Game to Develop Spatial Reasoning, and Analytical and Critical Thinking SkillsKevin Duchscherer 
This two or threeperiod lesson exemplifies Indigenous mathematizing in the form of a game that becomes an activity for learners to explore analytically in a way featured in the mathematics curriculum. In the first lesson (optional), learners follow authentic Plains Cree protocol to acquire three stones that serve as their markers in the gamef Picario. In the second and third lessons, learners play a simple form of the game and sequentially make the rules more challenging. They find patterns in the resulting strategies for winning. Finding hidden patterns in players’ strategies promotes twodimensional spatial reasoning. learners develop analytical and critical thinking strategies by posing their own problems to solve. 
Outcome WA10.2: Analyze puzzles and games that involve spatial reasoning using problemsolving strategies. 
Aspects of Cree First Nation Worldview (Sources: Sharon Meyer, North East School Division, FNMI: “Grandfather Rock,” 2014; “Medicine Wheel Teachings,” 2014; and “Tobacco Teachings.”) 
Water, First Nations Cultures, Statistics. ^{3}Kevin Duchscherer 
Grade 9 learners are introduced to the many and diverse roles that water plays in their everyday world and in First Nations cultures.Learners identify some social issues related to clean water.They are assigned a posterproduction project to communicate statistical information that sheds light on a social issue chosen by each learner. Critical thinking over how to recognize valid sources of statistics ensues. Formats for communicating statistical information are studied. Each learner chooses a format amenable to their poster’s statistics and defends their choice. 
Outcome SP9.4: Research and present how First Nations and Métis peoples, past and present, envision, represent, and make use of probability and statistics.Outcome SP9.2 Demonstrate an understanding of the collection, display, and analysis of data through a project. 
The circle is very sacred for traditional First Nations peoples.All ceremonies, celebrations, gatherings, and ways of thinking about the world are done within a circle format.For most Canadian First Nations peoples, the assumed direction sequence around a circle is based on the way the sun moves across the sky (clockwise). For the Haudenosaunee Confederacy (Iroquois), the sequence is the way the moon moves across the sky from day to day.Although the medicine wheel has four parts (in recognition of the sacred number four), everything within it is interconnected holistically. 
The Language of Negative and Positive Numbers^{4}Danielle Vankoughnett 
Three lessons demonstrate the integration of school math content (i.e., the number line and integers found along it) with authentic Indigenous contexts and with the school’s everyday world. 
Outcome N6.6: Demonstrate understanding of integers concretely, pictorially, and symbolically.Indicator b: Observe and describe examples of integers relevant to self, family, or community and explain the meaning of those quantities within the contexts they are found.Indicator d: Represent integers concretely, pictorially, or physically.Indicator g: Extend a given number line by adding numbers less than zero and explain the pattern on each side of zero 
First Nations children had names given to them associated with the elements of Mother Earth such as Rain, Sunrise, Raven, etc.Traditionally, First Nations families would have ceremonies that included the smudge to prepare a young man for his first hunt.Muskeg tea is a medicine that grows abundantly in Northern Saskatchewan areas.Tobacco, one of four sacred plants, is offered on different occasions along with words of thankfulness.Feasts are held to celebrate special occasions. Protocols are followed carefully so the feast is experienced in a good way.Sources of Indigenous knowledge brought into a classroom need to be authentic rather than hearsay. 
Stick Games and Theoretical/Experimental Probability^{5}Danielle Vankoughnett 
Based on patterns observed on Saskatchewan First Nations Pow Wow regalia, learners decorate six identical popsicle sticks on one side in order to investigate the theoretical and experimental probabilities that underscore a popsicle stick drop activity.Then by playing the more challenging Blackfoot Confederacy Stick Game with four authentically decorated popsicle sticks, learners solve probability problems and develop combinatory logic in order to solve a mystery surrounding the traditional Blackfoot game’s scoring system. Greater indepth learning about theoretical probability results from the game’s followup analyses. 
Outcome SP6.2: Demonstrate understanding of probability by: differentiating between experimental and theoretical probability; determining the experimental probability; and comparing experimental and theoretical probabilities.Outcome N6.9: Research and present how First Nations and Métis peoples, past and present, envision, represent, and use quantity in their lifestyles and worldviews.Combinatory reasoning and problem solving. 
Traditional Regalia is created by the dancer participating in a ceremony that includes fasting in order to receive guidance in creating the regalia for their selected dance. The vision quest type of ceremony guides the dancer to selected colours and patterns for their regalia. In current time, regalia patterns are being created without the dancer attending traditional ceremony. Contemporary regalia can express a dancer’s personal feelings, family identity, or relationship with a winged or fourlegged being..Just because a regalia pattern reminds us of a pattern familiar in math class (e.g., a triangle), it does not mean the pattern is a triangle. Instead, it will have a First Nations meaning indicated by the First Nations word that identifies the pattern. To know what that meaning is, we might ask the dancer (if possible). A Pow Wow is an event that celebrates all there is on Mother Earth. The dances are to give thanks to the elements (water, wind, fire, rock), the plants, and animals that sustain life for the human beings. 
Multiplication and First Nations Drumming^{6}Serena Palmer 
In this series of lessons, immersed in videos and firsthand experiences of First Nations drumming, learners come to a deep understanding of what mathematical multiplication actually means, from which some learners discover what division actually means. 
Outcome N5.2 Analyze models of, develop strategies for, and carry out multiplication of whole numbers.

The learners will learn about the importance of the hand drum including what the drums are made of, what they symbolize, when they are used, and why they are considered sacred. 
Quadrilateral Patterning through Indigenous Beading^{7}Serena Palmer 
Learners create a pattern that incorporates a quadrilateral in order to make a beading artifact. They draw their pattern on graph paper using coloured pencils. From there, the design is transferred to an 11strand loom by way of coloured beads. After the learners have made their beading artifact, they describe the attributes of their quadrilateral as well as of other learners’ quadrilaterals. 
Outcome SS5.6 Identify and sort quadrilaterals (rectangles, squares, trapezoids, parallelograms, rhombuses) according to their attributes.
Outcome SS5.7 Identify, create, and analyze single transformations of 2D shapes (with and without the use of technology). 
The learners will be able to (see Appendices A and C for more information):a) Understand that First Nations tradition of beading is a spatial mathematical process passed down from generation to generation.b) Understand that beading patterns often represent the family or the local area.c) List materials used by First Nations people to loom, before and after European contact.d) Explain the uses of beads in First Nations jewelry, art, and ceremonies.e) Describe the functions of beads and beading: as a form of money, to record agreements/treaties, to represent stories, and to decorate clothing.f) Create a beading artifact with an 11strand cardboard loom. 
^{1}Shemrock, K. Freestyle Looming and Probability – Grade 12 Foundations of Math. Retrieved 5 July 2020, from http://mcdowellfoundation.ca Access the resource here: https://saskatchewanmathca.files.wordpress.com/2020/12/1.ea.freestyleloomingandprobability.pdf
^{2}Duchscherer, K. Picario A Traditional Indigenous Game to Develop Spatial Reasoning, and Analytical and Critical Thinking Skills – Grade 10 Mathematics Workplace and Apprenticeship. Retrieved 5 July 2020, from http://mcdowellfoundation.ca Access the resource here: https://saskatchewanmathca.files.wordpress.com/2020/12/2.eb.1picario.pdf
^{3}Duchscherer, K. Water, First Nations Cultures, Statistics – Grade 9 Mathematics. Retrieved 5 July 2020, from http://mcdowellfoundation.ca Access the resource here: https://saskatchewanmathca.files.wordpress.com/2020/12/3.eb.2waterfirstnationsculturesstatistics.pdf
^{4}Vankoughnett, D. The Language of Negative and Positive Numbers – Grade 6. Retrieved 5 July 2020, from http://mcdowellfoundation.ca Access the resource here: https://saskatchewanmathca.files.wordpress.com/2020/12/4.ec.1thelanguageofnegativeandpositivenumbers.pdf
^{5}Vankoughnett, D. Stick Games and Theoretical/Experimental Probability. Retrieved 5 July 2020, from http://mcdowellfoundation.ca Access the resource here: https://saskatchewanmathca.files.wordpress.com/2020/12/5.ec.2stickgamesandtheoreticalexperimentalprobability.pdf
^{6}Palmer, Serena. Multiplication and First Nations Drumming. Retrieved 5 July 2020, from http://mcdowellfoundation.ca Access the resource here: https://saskatchewanmathca.files.wordpress.com/2020/12/6.ed.1multiplicationandfirstnationsdrumming.pdf
^{7}Palmer, Serena. Quadrilateral Patterning through Indigenous Beading. Retrieved 5 July 2020, from http://mcdowellfoundation.ca Access the resource here: https://saskatchewanmathca.files.wordpress.com/2020/12/7.ed.2quadrilateralpatterningthroughindigenousbeading.pdf
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