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Below, I discuss one of the five important ways that parents can help their child enjoy mathematics and do well in the subject. (1) Have a positive attitude towards mathematics, (2) Emphasize reasoning over memorization, (3) Reading is impactful, (4) Ask open-ended questions, and (5) Play mathematics games and puzzles. Emphasize Reasoning over Memorization If mathematics is conveyed to be about memorization then less students are able to be successful. Concepts are less likely to be retained and students number sense to determine the reasonableness of answers is diminished with a focus on memorization. Mathematics is not about how quick problems can be done but efficiency with understanding is great! Reasoning should be emphasized over memorization. There are multiple strategies for solving mathematics problems. With a basis of conceptual understanding students can become skillful in using procedures and strategies flexibly. One way that parents can encourage reasoning over memorization is by doing number talks with their child. Through number talks students can develop number sense and their math fact fluency. Number talks are becoming more prevalent in elementary grades mathematics classes and parents can also do them at home with their child. Number talks help students develop number sense and mental math abilities. In a number talk, a mathematical problem is posed and children are given time to think to solve the problem mentally. Next, all possible answers are shared for the problem without any statement about which is correct or incorrect. Children then defend an answer by sharing the strategy they used to solve the problem. Discussion occurs so that consensus can be reached on the correct answer and for students to hear the different ways the problem was solved. Number talks can involve one problem or a sequence of related problems. For example, a teacher may pose 28 x 5 and students may use the following strategies.  A sequence of problems could involve 8 x 5, then 20 x 5, and then 28 x 5 for students to get see the strategy of partial products. In a number talk, the goal is not to find the most complicated way to solve a problem, but to focus on strategies that build number sense, make use of related facts, and develop efficient, flexible strategies that can be used with accuracy. The table below has some strategies that parents can work on in discussing problems with their child. Having an idea of what answers make sense and how to separate and combine numbers flexibly can be developed with number talks. For example, solving 19 + 38 by taking one from the 38 and adding it to 19, making it 20 + 37, is an easier problem to solve. 
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Success in mathematics takes a collaborative approach. Teachers need to understand mathematics and how to teach it well. Students need to put in effort and work at becoming better learners. A child’s success in mathematics does not just depend on what happens in the classroom though. Parents can make a big difference in helping their children be successful in mathematics. In this post, I discuss one of five important ways that parents can help their child enjoy mathematics and do well in the subject. (1) Have a positive attitude towards mathematics, (2) Emphasize reasoning over memorization, (3) Reading is impactful, (4) Ask open-ended questions, and (5) Play mathematics games and puzzles. Have a Positive Attitude Towards Mathematics One of the most important things that parents can do is to demonstrate a positive attitude towards mathematics. One of the worst things that parents can say is, “I never got math.” When it is conveyed that mathematics is a subject that some students can do and others cannot, it can cause students to put forth less effort and accept that failing mathematics is okay. Parents can encourage their child that mathematics can be learned like any subject. They can also instill in their child the importance of mathematics to better understand the world and for decision making. When parents have a positive attitude towards mathematics and encourage their child they can do well in mathematics, it can make a big difference. The table below has phrases that parents and teachers should avoid as well as positive messages that can be communicated instead.   This activity integrates children’s literature, engineering design, mathematics, and English language arts. The children’s book I wrote helps students learn more about engineering and biomedical engineering. Biomedical engineering is an interdisciplinary STEM field that combines biology and engineering to create solutions for medicine and healthcare. English language arts standards are incorporated through reading the children’s book and a class discussion about the book. After reading the book, students work on an engineering design challenge to design and build a prosthetic leg. Mathematics is incorporated through measurement. After readings students the book, The Little Engineer That Could, the teacher then leads a class discussion using the following questions. Alternatively, these can be used as individual writing prompts. Describe Cadence and her feelings throughout the story. What was her motivation for helping Danny? How did her actions contribute to the sequence of events in the story. How did Cadence respond to challenges that arose? To begin the design challenge students watch the following video about the Invictus Games. The Invictus Games is an international sporting event for wounded, injured and sick Servicemen and women. The Games strive to use the power of sports to inspire recovery, support rehabilitation and generate a wider understanding and respect of all those who serve their country. After watching the video, students answer the following questions.
1. Why do you think the Invictus Games are held? 2. Do you know anyone who has been injured, sick, or hurt? 3. Why is important to help and encourage others? 4. Have you ever done something that was difficult? Why is it important to keep putting forth effort and to not give up? Challenge Sergeant Danny Mendez is participating in the Invictus Games. He wants your team to develop a comfortable leg for walking around the games when he is not competing. As a first step you will design and build the leg for one person in your group to test your prototype. Criteria and Constraints There are three criteria for the design. 1) The leg should be comfortable. 2) The leg should be sturdy and stable. The person in your group must be able to walk 10 feet with the prosthetic leg. 3) The prosthetic leg should be aesthetically pleasing (look good). Rubric for criteria 1) 1 point- leg is not comfortable and causes pain. 2 points- leg is mildly comfortable with little discomfort or pain. 3 points- leg is comfortable with little discomfort and no pain Rubric for criteria 3) 1 point-leg is not aesthetically pleasing 2 points- leg is somewhat aesthetically pleasing 3 points- leg is aesthetically pleasing The constraints are that you can only use the provided materials and that you have 60 minutes to design and build the prosthetic leg. Materials Your group will have scissors, measuring tape, and a ruler. -Duct tape -cardboard tube -pvc plastic pipe -large rubber bands -toliet plunger (unused) -wood board -sponge -bubble wrap -cardboard -string -rope Mathematical discussion is important so that students can learn from each other and explain their thinking. There are 5 practices for teachers to orchestrate productive discussion. A brief description of the 5 practices is below.
 -What was the big idea we worked on today?
-What did I learn today? -What good ideas did I have today? -What did I struggle with today? -Where could I use the knowledge I learned today? -What questions do I have about today's work? -What new ideas do I have that this lesson made me think about? A brief definition of mathematical modeling is real world mathematics problems that have more than one possible answer that students solve with choices or assumptions. The following information shows the benefit of mathematical modeling implementation in that all standards for mathematical practice can be integrated with mathematical modeling. Model-Eliciting Activities (MEAs) are one type of mathematical modeling activity.  This is a good open-ended problem that creates quality mathematical discussion. The median and the mean of the scores for Jenna and Kim are the same, which can require students to think of other possible solutions. A benefit of this task is that there is no one specific "correct" solution. There is also no prescribed method for solving the problem. Incorporating these types of problems leads to increased engagement and discussion in class.
----------------------------------------------------------------------------------------------------------------------------- There were five judges for a figure skating competition: The top two competitors were Jenna and Kim. They received the scores below. Jenna 8 6 10 9 7 Kim 9 9 7 8 7 Who should win? A teacher stood before a class of thirty senior mathematics students. Before he passed out the final exam he stated, “I have been privileged to be your instructor this semester, and I know how hard you have worked to prepare for this test. Because I am confident that you know this material, I am prepared to offer an automatic B to anyone who opts to skip taking the final exam.”
There was great relief for some. A number of students went right for the offer and thanked the teacher. “Last chance,” said the teacher and one more student went. The instructor then handed out the final exam, which consisted of two sentences. “Congratulations,” it read, “you have just received an A in this class. Keep believing in yourself."
This problem was given to 1st and 2nd graders and many tried to answer the problem by using the numbers in the question and picking a mathematical operation. If math is too focused on memorization then students are not seeing the power of mathematics. The following points should be emphasized with students when learning math. · 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 The following video has a similar problem done with 8th graders The following video has more details on the, how old is the captain problem. |
Micah StohlmannChristian, author, and professor of mathematics education. Archives
March 2022
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