Running head: MATH SUMMATIVE

Math Summative

By Emily Bass

Table of Contents

Annotated Bibliography …………………………………………………………………. p. 2

NCTM Article Reviews …………………………………………………………………. p. 5

Review of Five Math Manipulatives ……………………………………………………. p. 8

Mathematics Technology ……………………………………………………………….. p. 12

Areas of Interest …………………………………………………………………………. p. 14

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Annotated Bibliography:

1. Billings, E.M., Tiedt. T. L., & Slater. L.H. (2008). Algebraic thinking and pictorial growth patterns. Teaching

Children Mathematics, 14(5), 302-308.

The article opens by stating how algebra can be introduced to younger grades by familiarizing students with generalizing, which further develops their algebraic reasoning. One way to do this is by encouraging students to analyze and extend pictorial growth patterns (geometric pattern). More specifically, the authors examined and thoroughly discussed the strategies and reasoning processes young students use to analyze, extend, and generalize pictorial growth patterns. The article noted the importance of how teachers’ phrasing of questions can influence how students analyze patterns. In conclusion, the authors discovered that it was easier for children to analyze and extend pictorial growth patterns when constructed to look like recognizable figures.

I found this article to have many useful suggestions for introducing pattern concepts to students. Through researching, I have found that students are more likely to remember concepts when they see the connection and relevance to their lives. Considering this, when reading that students had an easier time working with patterns with familiar elements, it made sense that the students were more successful. I will refer to this article in the future, as creating a strong foundation of algebra is beneficial for students’ future learning.

2. Britton, B. (2006). Patterns galore. Teaching Children Mathematics,12(6), 296-298.

This articles provides examples of using a one hundreds chart from 0-99 to explore numerical patterns. The author explains how the typical one hundreds chart, being 10 number across and 10 numbers down, can be arranged in different shapes to find even more patterns. The author shares an example of the number of increasing patterns that can be found when the chart is arranged in a triangle, rather than a square. Britton suggests to let the students work collaboratively while exploring patterns so they are able to share their responses, and build on each other’s thinking. The article encourages communication and interaction between teachers and students for this type of activity, and also suggests for teachers to keep the explanation behind the patterns simple. Students are using many other mathematical skills to identify these patterns by calculating the differences among numbers, and identifying if the pattern is repeating or increasing. The one hundreds chart can be resourceful to further develop student’s algebraic skills. During my first practicum, the one hundreds chart proved to be a very effective resource when familiarizing students with numerical patterns. This article shares many ideas for teachers to use in the classroom, as well as suggestions on how to explain pattern concepts. Teachers commonly use the original 10x10 one hundreds chart when teaching math, but readers were able to see the added learning opportunities when rearranging the chart differently, as it allowed students to discover even more patterns. I

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appreciated the author’s support of collaborative learning, as I agree with the benefits of social learning.

3. Dubon, L. P., & Shafer, K. G. (2010). Storyboards for Meaningful Patterns. Teaching Children Mathematics, 16, 325-329.

The article opens by challenging teachers to think of how we can support young students as they develop concepts in patterning. The remainder of the article shares a teacher’s perspective and goal of introducing patterns through a meaningful approach. The teacher, Dubon, teamed up with a professor from a local university to teach patterns to her students. Through diagnostic assessment, they found that many students were still not able to create their own patterns, even after some instruction and similar prior activities. They decided to take a story-telling approach to make patterns more relatable to the students, and were surprised with the significant increase of positive results. The students found it useful to use coloured snap cubes to represent AB pattern elements, making the elements more meaningful to them. By using representations to guide their storytelling, students were able to create more complex patterns when also covering cross-curricular subjects, such as seasons. The author concluded by recognizing the importance of reflecting on her teaching practice, a process that proved to be valuable in reminding her of the importance of allowing students to attach meaning to all learning experiences. This article had very useful information. I strongly believe in making subject material relatable to students, so I enjoyed reading an article that was tailored specifically to my interests and beliefs. There have been numerous benefits proven from creating a connection between students and material, such as how it enables them to remember the concepts significantly better. The teacher and professor showed a good example of how to successfully collaborate in order to better meet students’ needs.

4. Hoffman, J., Ziemba, E.J. (2006). Sorting and patterning in kindergarten: from activities to assessment. Teaching Children Mathematics, 12(5), 236-241.

This article describes a teacher who desires to move away from the traditional use of worksheets. Instead, she promotes the use of manipulatives in her classroom when the students are exploring and creating patterns. Multiple manipulatives were listed such as shells, buttons, etc., as well as the numerous benefits of working with concrete objects. The author supports independent learning and considers herself a guide in the classroom. One of the ways she promotes self-directed learning is through facilitating a variety of learning centres. These centres allow students to discover mathematical concepts at their own level. Students are asked to reflect on their patterns by drawing and writing about them, which promotes the integration of literacy. The reflections also help the teacher assess individual student ability. Overall, the way in which the teacher manages the math centres proves to be very fun, interactive, and effective for students’ learning. My math lessons are very dependent on math manipulatives, so I have been able to see first-hand how they enhance student learning. This article would be useful for

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teachers who are unfamiliar with the benefits of math manipulatives, as it also provides specific examples of how to appropriately use them when teaching patterns.

5. Mattone, L. (2007). “ I know an old lady”: Using children’s literature to explore patterns. Teaching Children Mathematics, 14(4), 202-205.

This article discusses how children’s literature can be found useful in the mathematical classroom. The author shares her approach of using simple and engaging stories to introduce the concepts of patterns in the classroom. Books such as “I Know an Old Lady Who Swallowed a Fly” by Simms Taback enables teachers to discuss increasing patterns with students in a cross-curricular way. The article’s author found that one of the major benefits from using books such as these during math was that they allowed for students to practice skills in predicting and thinking abstractly. Students were also learning to describe the patterns numerically, verbally, and graphically. The author collaboratively created graphs and charts with her students that reflected the book’s patterns, so students were able to see a visual example. These strategies were used in kindergarten, proving to be effective for establishing a foundation of algebraic thinking. I encourage the use of cross-curricular resources, so I enjoyed how this article thoroughly listed the benefits of using these books for mathematical thinking. I think effective teaching incorporates many concepts throughout a lesson, and I am always looking for ways to interrelated subjects. Through personal experience as a student as well as a teacher, I Know an Old Lady Who Swallowed a Fly has always been a popular and engaging book that children enjoy reading. The article gives more examples of similar books that also enables teachers to promote mathematical concepts and vocabulary, allowing students to learn concepts through a variety of methods.

6. McGarvey, L. (2009). Matthew's thinking about patterns. Teaching Children Mathematics, 16(2), 126–128. This article explores the thought process of a young student as he uses his problem-solving skills to create a repeating pattern with specific coloured manipulatives. He was given three red, three green, and six blue tiles, and was successful in making an ABC pattern with some of the tiles. Through discussion and prompting, the teacher encourages Matthew to create a pattern using all of the tiles. The readers are able to see into Matthew’s thought process as he experiments with the tiles, quickly discovering how to successfully make a repeating pattern. Although this article is brief and in interview format, I consider it very beneficial to see the perspective of a young student. The article further resonated with me because I used this exact activity with my students during my first practicum while teaching patterns. When reading this article, I found Matthew’s thought process and reasoning skills to be very similar to my observations from my grade two class. I think it is important to try and gain understanding of your students’ thinking, so you are able to further guide and improve your lessons.

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NCTM Article Reviews:

1. Beatriz S. D'Ambrosio, & Signe E. Kastberg. (2012). Building Understanding of Decimal Fractions. Teaching Children Mathematics, 18(9), 558–564.

This article looks at the challenges preservice teachers faced when asked to arrange decimal fractions from least to greatest. For the number of individuals who were successful in this task, the authors were surprised by their inability to represent their thinking by using a decimal grid. A decimal grid proves to be an effective tool since most elementary students are already familiar with the resource. It is said to provide students with a representation to make sense of the connection between the symbolic representation of decimals and the decimal fractions themselves. The article continues by examining four preservice teacher’s different approaches to complete this ordinal task. They each used different reasoning when shading in parts to represent decimals, most showing evident difficulties and confusion. These errors were shown through pictures to provide visual aid, and were also well documented to be used for further understanding of common difficulties students face. From these errors, the authors identified three sources of difficulty when understand decimal numerals. Being aware of these difficulties allowed for the authors to provide guidelines and modifications when teaching to represent decimal quantities. Reading from a beginning teacher perspective, this article proved to be beneficial in seeing common errors other preservice teachers made with fractional math. The readers are also able to see the perspective and reasoning of students as they are working through a math problem, which is helpful when trying to teach fractional methods. This also gives teachers an idea of how to improve their teachings by seeing common difficulties. From a teaching perspective, the “sources of difficulty” component of the article may be found as most valuable. Knowing the underlying problems that lead to confusion creates insight for teachers to teach in a more effective way. The mathematical problem presented in this article is geared towards upper elementary, but the strategies shared by the authors can be easily adapted to use for lower or higher grades. Overall, the article reinforces that being able to transform numerals or symbols into other representations, such as number words, is essential in understanding decimal numerals. Making sure students are able to successfully practice this skill is necessary before moving onto more complicated concepts. The article was easy to follow and it clearly communicated how students use their reasoning skills for mathematical computations.

2. P. Holt Wilson, Marrielle Myers, Cyndi Edgington, & Jere Confrey. (2012). Fair Shares, Matey, or Walk the Plank. Teaching Children Mathematics, 18(8), 482–489.

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This article discusses how young students are often developing their fraction and division skills through daily activities. The authors provide examples, such as when students make sure equal parts of a snack is shared among friends, or assuring that everyone gets the equal amount of time with a toy. These simple activities requires children to think in terms of “fair sharing”. To further define this, the authors refer to the skill of creating equal-size groups or parts of collections as equipartitioning. The skill of equipartitioning requires children’s cognitive ability to partition a set of objects, or a whole into groups of the same size. For students to be successful in doing this, they must be skilled in the following three criteria: 1) creating the correct number of groups or parts, 2) generating equal-size groups or parts, and 3) exhausting the collection or whole. If students are able to gain these above skills, they will have a strong foundation when learning advanced concepts such as ratios, fractions, and they will become familiar with more mathematical strands. This article serves as a resource for teachers to see the perspective of students when rationalizing through fair-sharing activities. The article presents different methods and computational strategies that students use when developing the skill of fair sharing, which provides teachers with an idea of students’ thought processes. Through the author’s research, suggestions are offered on how to effectively establish a base for understanding rational number concepts through fair-sharing activities, and these can be easily adapted for any elementary or middle-grade skill. Overall, teachers can refer to this article when looking for fun ideas and activities to get their students engaged in fair-sharing math. The article provides concrete research that correlates with all findings and activities, and gives evidence that equipartitioning is crucial for students to further develop in various mathematical skills. Compared to other NCTM articles, I personally did not find this article as clearly laid out, but the information as still helpful.

3. Kelly K. McCormick. (2015). Making Fractions Meaningful. Teaching Children Mathematics,

22(4), 230–238. This article encourages teachers to challenge our knowledge of elementary mathematics, specifically fractions, so that next generation students to not experience the same learning that we did. Traditional teaching of mathematics was solely focused on memorization and rote learning, resulting in the limitation of our current knowledge and skills. The article looks at fourth and fifth graders explore fundamental fraction concepts, also asking pre-service teachers (PSTs) to solve the same problems while taking on young students’ perspectives. Readers are able to see pre-service teachers and students use various mathematical skills when discussing a fair sharing problem. Overall, I found this article very beneficial to read as a new teacher. The article provided many great points that should be brought into the classroom, such as using relatable fair sharing problems that can be found in real life examples. This allows students to see the relevance in the situation, resulting in findings the concepts easily relatable to their lives. The fair sharing problem that the article presents is equally sharing a sandwich among students. As the PSTs instinctively wanted to solve the problem using common denominators, they were encouraged to

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make sense of both the meaning of the numerator and denominator. Readers were brought along the process of the PSTs using their reasoning skills to figure out the fair-sharing problem; allowing them to make the same realizations, such as noting the importance of having the same whole when comparing fraction. Visual aids were provided to further understand the thought process. A significant take-away from this article was the importance of teachers placing themselves in the perspective of young students. Observing student’s initial discussions to problems allows teachers to see their reasoning, and guide teaching from there. From the PSTs experience, readers were able to see the effective mathematical learning that takes place when actively involved in a community of learning, collectively investigating and making sense of important mathematical ideas. Teachers should take this as an opportunity to promote collaborative learning in their classroom, while using real life examples to engage students. The article was easy to read and would not only be benefit to preservice teachers, but experienced teachers as well.

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Review of Five Math Manipulatives

1. Base Ten Blocks 2. Balance Scales 3. Pocket One Hundreds Chart 4. Snap Cubes5. Plastic Canadian Coins (or real ones!)

1. Base Ten Blocks

Base ten blocks are common math manipulatives frequently used in elementary schools. They can be used as an effective tool from kindergarten and all of the way through to grade five. Base ten blocks are composed of flats (represents 100), rods (group of 10), and one units (ones). For upper-elementary, there are also cubes that represent 1000. They are all measured by centimetre dimensions, which directly correlates with the Canadian metric system. The elementary years are the foundation for students to develop necessary skills in adding, subtracting, dividing, and multiplying. When computating with two digit numbers, these manipulatives can be used to teach regrouping numbers in order to reach an answer in the most effective way possible for students. Base ten blocks manipulatives are often considered essential when teaching students the above concepts. They are beneficial as they provide a visual aid so students can show their thinking process and final answer. They are made of hard plastic which serves as reliable aid for students to physically use. Having a concrete example is ideal for students to work with, and the manipulatives can be used for more advanced concepts such as measurement, fractions, and more. These manipulatives serve as a significant resource in every elementary math classroom.

2. Balance Scales

The balance scale becomes a key component in many elementary math concepts. This resource provides a great visual aid in order for students to further their understanding of the equals sign, as well as the concepts of greater than and less than. Objects can be placed on either side of the scale, allowing for students to be hands-on in their learning. Students should be

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encouraged to experiment with making the balance scale equal and non-equal. As noted in the text by Van de Walle, student problems in math and algebra commonly start by the misconception of the symbolism of the equal sign. The balance scale provides an opportunity for teachers to show students that equal really means “the same as”. By putting an equal number of the same objects onto each side of the scale, students can see that those two sides are exactly the same, and that is what makes them equal. If a student were to take one item out of one bucket of the scale, this enables the teacher to use vocabulary such as greater than and less than. This manipulative is useful because it could be incorporated into a number of different subjects. Students can directly see how making a change in the equation effects the end result. Balance scales can be used for a number of units such as addition and subtraction, weighing objects using the metric system, and more. Beyond working with the scale, students can physically draw a scale of their own on paper to represent various equations and numbers.

3. Pockets One Hundred Chart

The pocket one hundred chart become a frequently used manipulative when I was teaching math in the classroom. This is a great resource to have for limitless teaching opportunities. The chart features every number from 1 to 100, in columns and rows of 10 numbers. This enables students to see patterns and themes in numbers that are appropriate to their level. At first, this may just recognizing the pattern of counting be ones and skip counting by twos. Once the students are ready for further concepts, the one hundred chart can be used to show skip counting by fives and skip counting by tens in a way that is visually concrete for them. Having smaller one hundred charts readily available to students are helpful when they are first practicing addition and subtraction skills. This way, students are able to use their fingers to count 4 spaces back from 7, and see that the answer is 3. The students often requested one hundred charts when practicing the above types of computation. The chart can be used for a variety of games in order to encourage students to be familiar with number patterns. It can create multiple discussions such as the concepts of even and odd, rows and columns, tens and ones placements, greater than and less than, and how to order numbers. The benefits of having a one hundred chart in the classroom is endless as it is helpful to students of all skill levels.

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4. Snap Cubes

Snap cubes are another hands-on manipulative for students to explore a number of mathematical concepts, such as patterns, addition and subtraction, measuring, and spatial reasoning. The cubes come in squared centimetre dimensions, which directly correlates which the Canadian metric system. The cubes can be snapped together and pulled a part to build different lengths, providing an opportunity for comparing lengths to be visually appealing to students. The cubes are made of hard plastic, so they are durable for children to experiment with. The variety of colours creates an opportunity for discussing patterns. I have used snap cubes for students to build their own ten frame manipulative. Practicing with ten frames allows for students to become familiar with seeing a visual representation of the number ten, and any other number under ten. Knowing this skill, students can quickly visualize how many cubes are present, and then how many are missing (to make ten) without actually taking the time to count. I have also used snap cubes to teach the concept of creating a pattern core according to colour. These concepts are mostly commonly taught from grades K-2, so the manipulative would be found most beneficial in these classrooms.

5. Plastic Canadian Coins

Plastic or even real coins that align with Canadian currency provide a good resource and numerous benefits in the classroom. Coins can be used to familiarize students with counting money, which is an important life skill. Coins can also be used to reinforce students’ skills of skip counting, such as using nickels and dimes for counting by 5’s and 10’s. By grade two,

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students are introduced to using coins and skip counting, so having a concrete example to work with allows for students to enrich their understanding. Coins can be used to develop students’ skills in addition in subtraction, which numbers can make 100, and also using reasoning skills. Reasoning skills are used when students are asked to make “so many” cents out of a limited number of coins, and this also concept introduces the students to regrouping. Even though pennies are being faded out of the Canadian currency, I believe they can still be useful when practicing using ones in computations. For upper elementary, coins can be used as a manipulative when teaching decimals or fractions. Using coins is ideal because students are working with a manipulative that will be commonly used throughout their life.

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Mathematics Technology1. Brain Pop Jr.2. Math and Literacy Big Book3. Regrouping Using Base Ten

1. Brain Pop Jr.

Brainpop Jr. is a resource I frequently use throughout my teaching. The website provides a variety of resources for teaching students the general introduction of mathematical concepts. For each concept there is a featured video with a corresponding game, activity, comic strip, and more. There are options for the mathematical concept to be incorporated into literacy, such as opportunities to write about it, read about it, a word wall page, as well as a place to draw about it. There are printable activities that the students can do individually, and the quizzes could be done collectively by the whole class. This way, the concept is covered in a variety of different ways which reinforces the students’ understanding. One of the most valued benefits of the website is the “lesson ideas” available for teachers. These ideas give many suggestions for activities that can be easily adapted to include in a classroom. I have referred to this website if I am ever seeking to better my lessons by making them more creative and interactive. This site does require

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a membership and with a fee, but the cost is well worth the resources you get in return. The website is easy to use and the characters remain consistent, allowing the students to become familiar with them. Since the website can be easily used by all ages, an upper elementary student could maneuver through the site and learn at their own pace. I have shared this resource multiple times with students, and they always express their excitement when seeing the characters explain any given concept. Luckily, Brainpop Jr. is not only limited to math but also has activities in different subjects, such as literacy, science, and more.

2. Math and Literacy Big Book The following is a video of a big book I created for a math creative project. This book is effective for teaching math but it also incorporates literacy. The math component introduces basic shapes, which would pertain to a kindergarten level or below. The literacy component is a little more complicated than the shapes, but the language could be practiced by any upper Elementary student. Please copy and paste the following link into your browser if the below video does not play:https://youtu.be/cqkBY1rg4HI

3. Regrouping Using Base TenIn the following video, I am explaining how to regroup by using base ten blocks. The examples show addition of two-digit numbers, but the concept can be easily adapted for any grade level. Please copy and paste the following link into your browser if the below video does not play:

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https://youtu.be/gb_WibPcCHU

Areas of Interest

1. Children’s Literature 2. Science Observation Journal3. Math Reflective Questions4. Kinesthetic Learning

1. Children’s Literature My Little Sister Ate One Hare

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“My Little Sister Ate One Hare” by Bill Grossman serves as a great cross-curricular resource when familiarizing young students with patterns. Ideally for grades K-2, this book introduces the concept of patterns. The book quickly engages young readers be describing the story of a young girl eating one hare. With each page, the girl is continually eating one more thing than the number of peculiar items she ate before. The story builds from eating two ants and progresses all of the way to eating 10 peas, creating opportunities for teachers to introduce discuss increasing patterns. For example, after reading how the little sister ate five bats, the teacher can ask students if they know how many things she will eat next. How do they know? This also allows for the teacher to discuss related mathematical vocabulary. Building from student responses, the teacher can explain that the pattern is increasing by one element every time, as the little girl eats one additional thing compared to last time.

Whole-y Cow! Fractions Are Fun

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Written by Taryn Sounders, Whole-y Cow! Fractions are Fun promotes learning fractions in an engaging way. The readers follow one whole cow as it embarks on a number of adventures, each prompting students to answer which fraction is being portrayed. Starting with ½ of the cow being painted blue, the book progresses into exploring fractions of thirds, fourths, eighths, and tenths. The book is very interactive and would be beneficial in a read aloud setting for introducing fractions. This book would be ideal for middle elementary, anywhere from grade two to grade four. The book also proves to be comical and entertaining, while providing cross-curricular connections to literacy. Written in poem form, students are practicing literacy skills such as rhyme while also familiarizing themselves with mathematical concepts. This provides a great foundation for teachers to further build on fractional concepts.

1. Science Observation Journal

This journal was a required assignment for our science class, however, it is cross-curricular with math. The observation journal includes many mathematical concepts and outcomes, such as measurement, data analysis, graphing, and more. Assignments such as this allows students to express their learning through a number of creative outlets and areas of interests. It also enables students to be interactive with the environment by monitoring rainfall, animals, plant growth, and whatever peaks their interest. By using different methods to record observations, students are practicing numerous mathematical skills while being engaged in their learning.

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2. Reflection Questions

At the end of the Van de Walle textbook, Elementary and Middle School Mathematics, some of the questions prompt readers to further reflect on given mathematical practices. The following responses share my personal experiences and approaches pertaining to concepts of the corresponding chapters.

Chapter 15: Developing Fraction Concepts +1 Question: A common error that students make is to write 3 over 5 (3/5) for the fraction represented below. Why do you think they do this? What activity or strategy would you use to try to address this misconception?

Answer: I believe students may make this common error because they are unfamiliar with the concepts of numerator and denominator, and what exactly they represent. When students see the three boxes coloured in, they can make an assumption that it is the numerator, but they are unsure how it relates to the whole. From looking at the picture, they believe that 3 wholes will always be present. They would then count the leftover boxes, incorrectly calculating five as the denominator, or a separate whole. They have not yet developed the skills to see how the two numbers are in relation to each other. They are viewing the numerator and denominator as two separate pieces rather than representing one fraction. To try and address this misconception, it is important reinforce activities that remind students that the denominator represents the whole unit, and that it tells the sized part that is being counted.

Chapter 21: Developing Concepts of Data Analysis +2 Question: The process of doing statistics must be clear to students, even when they are working on a piece (ex: circle graphs) within the process. Pick a grade, and consider possibilities for authentic and engaging (and researchable) questions. Then discuss how you would plan instruction in order to include the four-step process and engage students in statistical thinking.

Answer:The process of statistical thinking:1. Formulate questions-clarify the problem at hand-formulate one or more questions that can be answered with data2. Collect data-design a plan to collect appropriate data-employ the plan to collect data3. Analyze data-select appropriate graphical and numerical methods-use these methods to analyze the data

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4. Interpret results-interpret the analysis-relate the interpretation to the original questions             During my first practicum, I did a data analysis unit with the grade two students. They worked on collecting data within their own classroom, based on each students’ personal response. As it was an introductory unit, the questions were already given to the students in a packet. Therefore, the first stage of statistical thinking was mostly already done for them. These questions prompted for specific answers that the students could choose from. For example, one question might be “What is your favourite flavour of ice-cream? The choices would be, “vanilla”, “chocolate”, “strawberry”, and “neapolitan”. For the second stage, collecting data, the students were encouraged to personally go around and ask questions to each student. For analyzing the data, each page of the packet had a different method of collecting data, such as using tally marks, or colouring in a bar graph. For the students to interpret results, they were able to see a visual representation of the data they had collected. They could see the highest coloured column on the bar graph and relate it to what activity was most popular to do on the weekends, and so on.

4. Kinesthetic Learning

I believe that actively involving students in their learning process has endless benefits. Activity in the classroom is proven to increase memory, collaborative skills, social skills, and more. It also enables students to see the personal connection that can be made to their own lives. Students appreciate knowing how the concepts are relatable to them, and they will find their learning more useful. I am going to discuss two examples (of many!) that were improved through incorporating kinesthetic learning in mathematics.

Graphing Unit: When teaching students about graphs, there are endless opportunities to use classroom involvement to enrich learning. When introducing the concept, I asked students to arrange themselves in different “categories” to show different ways we can make a graph. One of the activities we did was dividing ourselves by hair colour. We started with blonde, brown, black, and red. The students arranged themselves in four different lines, showing the differences. By using the students’ bodies, we were able to explain that we were representing a concrete graph since we are using physical objects that we can arrange, manipulate, etc. There are a number of ways a teacher could adapt this activity of asking the students to make lines depending on eye colour, etc. Having the students physically make the graph using their bodies allowed them to see the relevance and a clear example of the concept. To introduce the concept of another graph, such as a pictograph, I handed sticky notes out to each students. I asked the students their favourite kinds of Christmas treats (it was December), writing a few of the common responses on the board. Students had to refer to the four choices on the board, choose one they prefer, and draw it on their sticky note. From there, they went up and stuck their picture to the corresponding “treat”. This gave students a visual representation of the different preferences, enabling the teacher to discuss vocabulary such as “the majority, more than and less than”, and more. Since the students are drawing pictures, the teacher can reinforce that

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this is a “pictograph”, since it us using pictures.

Data Analysis Unit: When introducing data analysis to the class, using activities that required participation was beneficial to my teaching. When practicing different methods of collecting data, such as tallying or colouring boxes for a bar graph, the students enjoy gathering information from their peers. Each page of a student packet would ask a simple question, such as “What is your favourite thing to do on the weekend?”. The students were given choices to choose from, such as 1) go see a friend 2) sleep in, 3) go shopping, or 4) play outside. Students would spend the class interacting with their classmates and recording individual responses. The students found this activity fun as it was relevant to them, and they could learn more about their peers. The following pages asked students to find more data based on their classmates’ personal opinions, past-times, and more. It was a very interactive way for the students to learn the concepts, and it promoted student-centered learning.