Teaching Canada in the United States

Kristen Barry is a senior and majoring in Elementary Education, with Math and English as core subject areas. Kristen's essay integrates Canada in a Mathematics curriculum (not easy), by suggesting that even math can be used to bring a broader international perspective to students. She presents clear examples of how this can be done by activities like graphing the Canadian population and learning the metric system.

Teaching Canada: Mathematics

Kristen Barry

In education, students learn concepts of multiple subject areas. Often this knowledge is applied to their daily lives and personal experiences, which makes this new information meaningful. When students find pertinence in learned concepts, the likelihood of retention is greatly increased. As students continue their education in the United States, they learn about math, literacy, social studies, and science as it relates to life and culture in the United States. Although it is crucial for students to understand academic information in regard to their country of residence, awareness and knowledge of other societies and nations is important as well. In order to achieve students' broader international awareness and required academic information, teachers may present academic concepts to students in a way which shows how those ideas relate to the everyday lives of people from other nations as well as those from the United States. As one of the two countries that directly border the United States, it is especially important for students of the United States to be aware and understand how Canadian citizens and society impact that of the United States. While it may initially be considered to be difficult to incorporate this information into curriculum outside of social studies, there are many ways to integrate teaching about Canada into other subject areas. Focusing on math in particular, students from kindergarten through seniors in high school in the United States may be taught about the various aspects of Canada through the different domains of mathematics, which include geometry, arithmetic, algebra, critical thinking, measurement, estimation, graphing, and fractions.

Prior to considering explicitly which material to teach in mathematics as it relates to Canada, an educator must consider how children learn as well as which information would be the most important for them to know about Canada. As previously discussed, concepts that are made meaningful to children are more commonly retained. Therefore, if a teacher were to create engaging and interactive experiences to teach about Canada in a mathematics course, students would be utilizing multiple learning styles and forming connections of their experience in the classroom to how mathematical concepts may be used in Canada. Additionally, students and people in general learn by thinking of ideas as concrete and then progressively move to considering concepts to be more abstract and interrelated. Utilizing this model for progressive learning, an educator could introduce a new mathematical idea in a concrete manner such as by providing an experience or specific example. This concrete instance would be an opportune moment to incorporate lessons about Canada as well. The teacher could consider how this mathematical concept is used or related to information about Canada, and employ that information to teach a lesson about math. The facts and notions about Canada that may be addressed in math classes in kindergarten through twelfth grade in the United States include population, trade, culture and society, conversion to the metric system, comparisons between the United States and Canada, Canadian landmarks and buildings, Canadian government, exchange rates between money in the United States and Canada, Canadian geography, and economics in Canada. Although this list is not a comprehensive list of topics that can be taught about Canada in pre-collegiate mathematics courses, the items on the preceding list may be encountered by students in the United States, especially those who may live near the Canadian border or visit the country on a trip.

Graphing is a mathematical topic that could be used to teach American students enrolled in various grade levels about Canada. There are different kinds of graphs including bar graphs, pie charts, line graphs, and scatter plots that may be used to visually represent qualitative and quantitative facts. While teaching students the various ways to graph data, this could be an appropriate time to integrate lessons about Canada into a math class. When initially learning to graph in lower elementary school, students may represent quantitative data of a small value on a number line. For example, while learning about Canada, students may plot the number of provinces on a number line, as well as the number of Canada's territories on another number line. A map of Canada may be shown to students in order to point out the different provinces and territories. The teacher may also accompany this depiction of Canada on the map with a short explanation of the differences between provinces and territories. Students may then move to creating bar graphs and plot out the number of provinces and the number of territories this way. Bar graphs may also be used to show comparisons between the United States and Canada in areas such as population, land area, gross domestic product, ethnicity, demographics, percentage of common natural resources used, and other shared aspects. Further, a bar graph could show the different proportions of the population in Canada speaking English, French, and other languages, or how the frequency of these languages spoken has changed over time. Bar graphs may also show the results of survey questions asked of Canadians about their culture or lifestyle such as divisions in the population based on age or gender, or what Canadians commonly like to do in their free time or favorite sports. Students may find themselves as similar to such responses from Canadians.

As students advance in their graphing capabilities to learning to plot points using an x-axis and a y-axis on a coordinate plane, they could start by graphing information as individual points as a part of a scatter plot. A scatter plot allows students to practice plotting individual points and finding whether or not there is a trend between those two points. Educators could provide students with a list of Canada's population as it has changed from year to year or every ten years. As another tactic to having students practice plotting points on a coordinate grid, teachers may give students a list of points to plot on the graph. If a student were to connect sequential plotted points by a line, an image could be created that represents something in Canada. One such example would be for students to plot points on a graph to create an image of the Canadian flag. Once students have mastered plotting points on a coordinate plane, they may move onto creating line graphs. A teacher may give year to year or every ten years. Students may then see how the population in Canada has changed over time. Older students who are able to identify a change in the population of Canada may then participate in a guided discussion with their teacher about reasons for decrease or increases in population.

As students continue to progress in their graphing knowledge and abilities in middle school and high school, they will eventually be able to graph algebraic, trigonometric, and calculus functions, and analyze this information to explain the solution to the problem. In order to teach about Canada while using such functions, a teacher could create a theme related to Canada while presenting how to solve, graph, and analyze such functions. The teacher could then make some word problems directly related to the theme about what he or she is currently teaching about Canada that also utilizes the mathematical concepts. For example, an algebra teacher may select the theme of international trade in Canada. Students who are working with parabolic functions may be provided with a word problem that requires the student to find the maximum amount of profit a Canadian oil drilling company may have due to shifts in oil prices over the period of a year. The teacher could also provide word problems with other Canadian exports that earn a profit to give students multiple opportunities to practice the math concepts as well as learn about additional Canadian exports. In this example, students are learning how to solve parabolic functions, graph the results, and analyze the representation, while simultaneously learning about Canadian exports and profit from goods.

Another way to integrate information about Canada into math classes in the United States is to focus on Canada's use of the metric system. Early elementary school students may first be exposed to the metric system by incorporating rulers and other forms of measurement that use metric units. Young students may use metric rulers to measure items in the classroom. Teachers may also introduce students to the metric system through a cooking activity while using metric measuring cups and weights. The dish that is being cooked could even be a popular Canadian dish so students can concretely experience forms of measurement used in Canada as well as a common food in Canadian culture. Once students have been exposed to various metric units as used in Canada, they will have a sense for what each metric unit looks like in length, feels like in weight, or holds in volume. Therefore, students may then start applying estimation in regards to the metric system. For instance, children may pretend they are going to a doctor in Canada to determine their height and weight. Children could first predict their height and weight in metric units, and then find their actual height and weight through the use of a meter stick and scale with kilograms as the unit. Students can also estimate long distances in kilometers, such as the border of the United States and Canada.

As elementary students master the metric system, they can begin to compare measurements of objects in metric units to those measurements of the same objects in the customary system, which is used in the United States. This will prepare students to start converting measurements mathematically from metric units to customary units and vice versa. Once students advance in mathematics to middle school and high school, they can start converting between the different systems of measurement. In order for students to practice converting between measurement systems, teachers may provide students with a variety of activities and scenarios that would require them to use conversion. For example, a teacher could plan out a hypothetical trip for students to travel from their current location to a major city in Canada, such as Toronto. The teacher could provide students with the distance in miles and have students calculate the distance in kilometers. Then to extend the lesson, students could prepare a route with the distance in miles and kilometers to five additional locations in Canada. Students may also practice converting miles per hour to kilometers per hour if they were to drive to all the locations on their trip, and how long it would take for them to arrive at each destination while driving a constant speed. In addition to converting distances and speeds, students can practice converting between Canadian money and money from the United States. This would be a useful exercise for students because they would practice the mathematics of converting the equivalence between two different money values, but also because of how they may have observed the differences in prices listed on price tags. Often price tags in the United States list the American value and the Canadian value of the item.

In addition to converting between the metric and the customary measurement systems, an educator can teach about Canada through geometry. In early elementary, students can identify the shapes of famous buildings in Canada. For example, teachers can provide students with an image of Toronto's skyline. Children in the class can identify the different shapes they see and how these shapes construct the buildings. As children progress through their geometric knowledge, they will advance past identifying basic shapes to determining areas and characteristics of shapes. Upper elementary students can find the land area of Canada as a whole as well as its individual provinces and territories. Further, upper elementary students can practice using a protractor to discover the angles of shapes comprising famous buildings and landmarks in Canada. Through such an activity, teachers can have a guided lesson about how the internal angles of polygons like triangles and quadrilaterals become a certain total every time. Also, educators can address how the shapes students are measuring in the pictures of the buildings are similar to the real life shapes comprising the Canadian buildings. Students can learn that although the shapes in the image are smaller than the shapes of the actual Canadian buildings, they are similar because the lengths of the shape's sides are proportional and the angles are the same. Eventually, students will reach a point in their geometric education in which they learn the Pythagorean Theorem. Teachers may use examples of buildings in Canada forming right angles with the ground, which would be one leg of the triangle. Then the shadow cast upon the ground would be the other leg of the triangle. Given both lengths, students could determine the length of the hypotenuse, or the length from the top of the building to the edge of the shadow. Further, when students progress to trigonometry, they can use functions to determine the angles of such a right triangle formed by a Canadian building. By using Canadian buildings, students are learning the math concepts as well as important landmarks in Canada.

Another method for students to learn about angles in geometry is for students to interactively participate in one of Canada's most popular sports, hockey. Students can learn about alternate interior angles, in which when a line passes through another straight line, the angles formed diagonal from each other have the same angle measure. This concept can be demonstrated to students by shooting a hockey puck at a wall. When the hockey puck rebounds off the wall, it moves away from the wall at the same angle at which it came toward the wall. Once students have participated in this activity, the teacher can give students the assignment of acting as a hockey coach for a Canadian team. Students will be required to design plays for their team in which they have to consider and incorporate various angle measures and alternate interior angles. The teacher may also integrate ideas about how hockey is part of Canadian culture into his or her lesson. During this lesson, students will be practicing methods of a sport popular in Canadian society and relating it to geometric principles.

By teaching students in the United States about Canada through specific and interactive lessons in mathematics, students of all ages will be able to grasp both mathematical concepts and knowledge about Canada. As students become engaged in the lessons or have a precise instance to relate a mathematical concept to Canada, they will more readily be able to recall the details and mechanics of the mathematical idea. Further, students will be able to expand their knowledge of a country located near their own. While the preceding paragraphs provide multiple examples of how students can learn about Canada in math class, all options are not listed. There are still multiple ways a teacher can include information about Canada in math lessons. For example, a lesson that requires students to formulate a budget for Canada while acting as members of Parliament would provide students with the opportunity to learn about Canada's government, factors that influence the country's national budget, as well as the math skills necessary to compute that budget. Students could also learn about ratios, fractions, and percentages by comparing population, demographics, area, amount of land and water, and other factors in Canada. From kindergarteners to high school seniors, the list of possibilities for teaching about Canada in mathematics classes is endless. Students may simultaneously learn about math and Canada as long as the teacher is willing to create lessons that integrate both ideas. Such incorporation would be beneficial for students because of the meaningful experiences that would be created as well as the extension of students' knowledge of the people and the country neighboring their own.

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