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The game, Bigger or Better, is now a book! Each team starts with the same item. They then must go out and find people that are willing to trade something for the item. The goal is to end up with the biggest or best item. Which team will win? This fun and lively book will keep children engaged! Check the back of the book for ideas on how to develop children's number sense for fractions!  Comparing fractions When two fractions are not equivalent but are parts of the same whole or unit, there are several ways to find which is greater through comparison. It is important that the fractions refer to the same whole or unit though. This could be comparing a fractional amount of a pizza to a fractional amount of a pizza the same size. Other examples that are possible are to compare length in feet versus length in feet, area in feet squared versus area in feet squared, or comparing weight measured in pounds. However, comparing fractional amounts of two different units can be difficult to do. For example, 1/3 of a cake versus 4/5 of a chocolate bar. 4/5 is a larger number than 1/3 but the cake may actually be bigger in size compared to the remaining chocolate bar. Comparing fractions using concepts 
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A recent review of studies that involved game-based learning found that most of the games used in the studies involved drill and practice. In drill and practice type games, students only receive feedback on if answers are correct or incorrect and do not receive support for conceptual understanding. These types of games also emphasize that mathematics is about speed and focus on memorization of ideas instead of conceptual understanding. Game based learning for mathematics should move beyond drill and practice. My principles for technology game-based learning ensure that games are selected and implemented with best practices for teaching mathematics in mind. First, the technology integration should allow for significant task redesign or the creation of new tasks that would not be possible without the technology. Second, the tasks used should be worthwhile tasks. These tasks have no prescribed rules or methods and there is no perception that there is a specific “correct” solution method. Third, the tasks should be aligned with grade-level standards. Fourth, the tasks should enable students to work with multiple representations. Fifth, the technology should provide students feedback. Finally, the tasks should be open-ended and allow for discussion and multiple solutions (Stohlmann, 2019). When structured well, technology-based mathematics games can engage students in mathematics and help develop their conceptual understanding. Reference:
Stohlmann, M. (2019). Integrated steM education through open-ended game based learning. Journal of Mathematics Education, 12(1), 16-30. Rigor
Students should do mathematical work that is challenging with feedback and any needed scaffolding. Students should have the opportunity to demonstrate understanding in different ways. High expectations are key. Relevance Students should see the power of mathematics and understand how mathematical knowledge is relevant to their current and future lives. Relationships When students know that their teacher believes in them, cares about them, and wants them to succeed it makes all the difference. In context game-based learning games are used as an interesting context to pose mathematical problems. When students play the mathematical context games, they are not doing mathematics but do solve mathematical problems related to the games. For example, in the water bottle flipping activity students play a game to see how many times in a minute they can flip a water bottle and get it to land straight up. In the activity, students do five one minute trials in which they record how many lands of the water bottle they can make in one minute. The world record for this is 47 lands in one minute. Based on the five trials students then calculate their average number of lands per minute. Students then fill in a table based on this average and answer follow-up questions (Figure 1). The activity has students work with proportional and linear equations through tables and equations. In the whole class discussion after students have answered the questions, connections can also be made to the graphs of students’ equations and interpreting the graphs in the context of the game. Questions can also be posed to compare equations in regards to slope.  The context of water bottle flipping engages students and allows for interesting questions to be asked. Students are able to interpret mathematical answers in the context of the game and make connections between representations. Another example of context game-based learning is the paper basketball activity. In this activity students estimate and calculate how many paper balls will fit into a bucket. After doing the mathematical work students then race to see who can make the most shots of paper balls into the bucket in a minute. This game is engaging and motivates the mathematical work through different representations that incorporates measurement, mean, volume of spheres, and linear and proportional equations. Doing mathematics in the context of games engages students through interesting mathematical work, movement, and healthy competition.
Class closers allow for a quick assessment to see what students have learned and the teacher can connect the ideas back to the stated objectives from the start of the class to review if the objectives were met. Below are some basic examples and following that are some more creative ideas to mix things up every now and then.
    Of all the fourth graders at Fairview Elementary the twins, Tony and Tina, were known for their ability to make friends. They enjoyed school but struggled with mathematics. After learning more about the importance of mathematics, Tony and Tina strive to help their classmates have the right mindset. Find out how Tony and Tina's ideas lead to mathematical success for themselves and their classmates!  “You teach math? Oh I never got math.” I have heard the following comment so often, that I decided I would try to do as much as possible to change this sentiment. Mathematics is a subject that has the stigma that some people are “just not math people”. This is a dangerous idea that needs to change. While everyone will not go into a math heavy career, everyone is capable of doing mathematics. The life skills including teamwork, communication, and being synthesizers of information that students can develop from mathematics will help in any career as well.
Mathematics education can be improved with little things that could cause a tipping point. A tipping point is the moment at which ideas and messages can spread very quickly to cause change. Eliminating the phrase, “I never got mathematics” and replacing it with the phrase, “You can do math. I can do math” is a good start to improving mathematics education for all. Beliefs are the best indicators of the decisions that people make over their life-time. By giving children the right mindset at an early age, they will be set up for success! Mathematics and exercise, what a great combination! The title of this book has two meanings. Children can learn effective ways to group and add numbers through this book. Also, the book extols the benefits of exercise throughout one's life. This wonderful book is fun for children and adults! Pluses of Pilates encourages students to combine numbers in groups of 5’s and 10’s for easier adding. Children need experiences to see how to count things quicker than just counting by one’s and can work on number facts through reasoning while doing this. My view on the teaching and learning of mathematics is based on the points below and should be encouraged and instilled in children at a young age. · Everyone can do math! · Emphasize reasoning over memorization · Encourage multiple strategies and ways of thinking · Math is not about how quick problems can be done but shortcuts with understanding are great! · Encourage discussion and exploration · Math should foster curiosity · Math should be relevant and realistic Exercise is important for your whole life. Keep in mind the basics below for continuing to exercise and be healthy. · Find an exercise routine that you enjoy · Incorporate variety in your routine · Eat healthy and drink plenty of water in addition to exercise · Do not go 3 days without exercising   Ben and Julie's parents have some questions for them before they will be able to get a dog. Meanwhile, Hesed, the husky, also has questions about his new home. Will Ben and Julie pass the dog interview? The mathematics of area, perimeter, and geometry are incorporated in this wonderful book.  The relationship between area and perimeter
Area, the two-dimensional space inside a region, and perimeter, the distance around a region, are continually a source of confusion for students. This is in part because students may simply be given formulas to use and not understand the concept of area and perimeter. The two activities below are useful to help students understand area and perimeter. Activity #1 Give students a loop of non-stretching string that is exactly 24 centimeters in circumference. The task is to decide what different-sized rectangles can be made with a perimeter of 24 cm. Students can be given 1 cm grid paper to place their string on. Each different rectangle can be recorded by students with the area calculated. Students can also do this activity with just the grid paper by being asked to find rectangles with perimeters of 24 cm. Activity #2 Provide students with centimeter grid paper. The task is to see how many rectangles can be made with an area of 36 cm squared. Each new rectangle should be recorded by sketching the outline and the dimensions on grid paper. For each rectangle, students should determine and record the perimeter as well. An escape room is a game in which teams solve multiple puzzles using clues, hints, and strategy in order to figure out how to escape from a locked room. It has been found that the use of puzzles and gamification in mathematics increases students’ participation and engagement. The prevalence of escape room businesses has increased in recent years. Escape rooms used in the classroom can provide an enjoyable and memorable challenge for students as they work together in teams. Incorporating escape rooms is one way to engage students, encourage productive struggle, and foster teamwork. In designing and classroom testing escape rooms I have developed important principles for preparing escape rooms to be used in the mathematics classroom. These include a unifying theme and a brief backstory, structures to help students persevere in problem solving, and a compelling twist. The backstory provides information on the context of the problem and what students must do to finish the escape room (Stohlmann, 2020).  Students that participated in the escape rooms have enjoyed the mathematical work situated in a fun challenge and they were able to persevere in problem solving by demonstrating many characteristics associated with a growth mindset. Students commented that the time went by quickly as they stayed focused on completing the escape room. As groups worked on the problems they shared their mathematical thinking and developed their knowledge (Stohlmann, 2020). Students also felt a sense of pride in the work and effort that they put forth. For example, a student at the conclusion of one of the escape rooms commented, “I feel so accomplished!” I have also written a book based on the Michael's Movie Moves escape room with example student responses that highlight a variety of strategies that students can use to solve ratio and proportional thinking problems. Included in the book is useful information for teachers and students on proportional thinking strategies including scale factors, tables, unit rates, tape or strip diagrams, double number lines, pictures, equations, and graphs (Stohlmann, 2019). An example from the book is below.   References:
Stohlmann, M., & Kim, Y.R. (In press). Game-based learning: Robotics and escape rooms. The Australian Mathematics Education Journal. Stohlmann, M. (2020). Escape room math: Luna’s lines. Mathematics Teacher: Learning and Teaching PK-12, 113(5), 383-389. Stohlmann, M. (2019). Escape room: Michael’s movie moves. Seattle, WA: KDP. There are several important things to keep in mind when selecting an integrated STEM lesson and preparing to engage students in integrated STEM education. When selecting an activity keep the mathematical objectives in mind. It is important that grade level mathematical topics can be used and that they are aligned to the mathematical objectives. This can be done by anticipating possible student solutions to the tasks. If students do not use the all the intended mathematics, teachers can share additional ways of thinking about the task and make connections to students’ ideas. It is also important to consider if students will understand the problem context. If the problem involves an unfamiliar realistic context, this could hinder students’ work. If teachers are new to integrated steM education, another important point is to select classroom-tested lessons. These may also include possible student solutions to help with anticipating. Students can be supported to productively engage in integrated STEM education with messages before participating, while participating, and after participating in integrated steM. Teachers can share the following messages with students to prepare them for the work they will do.
While students are working, teachers can monitor the groups to see what ideas groups are using. Teachers can also provide feedback to ensure groups work well together. The following messages are important to reinforce while groups work.
When the time for groups to work is complete, students will be interested in hearing how other groups solved the problem. Teachers can let students know to listen for connections between the ideas. Students can also be given time to reflect on what mathematics they used, how well they understand it, and how well they did working in a group. In summary, it is important to carefully select tasks by anticipating possible student ideas, utilizing cooperative learning, supporting students with important messages about integrated steM education, and having whole class discussion on students’ ideas |
Micah StohlmannChristian, author, and professor of mathematics education. Archives
January 2021
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