Mathematical Processing and Problem-Solving In Mathematics Classrooms
Hi everyone, and welcome back to my blog!
This week's lesson focused on the importance of instilling problem-solving skills in high school math students. We focused on the differentiation between various problem-solving strategies that were established by Polya and Doxiadis. Our class discussion regarding problem-solving strategies really evoked many practical aspects of the teaching profession. Personally, I felt like our discussion helped me in my tutoring with high school students. I sometimes feel that I am 'stuck in my ways' when it comes to teaching certain material. However, this class in specific has really challenged me to seek different ways in explaining specific math concepts to students. For example, techniques such as drawing a picture, or writing out lists of possibilities for a solution are strategies that I will implement into my own tutoring practice, and in my future classroom. Thinking Mathematically emphasizes the importance of students 'being stuck' and how problem-solving strategies will ultimately benefit them as students and help them through the 'being stuck' process, which is an important piece of the learning process (Mason, Burton & Stacey, 2010). Therefore, I feel like discussing problem-solving strategies is something I need to improve on as a professional. Attached is a brief list of problem-solving strategies that I found:
We also discussed how student attitudes are imperative when teaching problem-based learning strategies, and how using a three-part structured lesson plan can maximize problem-solving capabilities of students. A question that I have is how can I get students more engaged in the problem-solving process? Although strategies such as a gallery walk can be useful for some students, what other strategies can be implemented for those students who may learn in ways other than visually? What can we do as mathematics educators to be inclusive of logical, interpersonal and linguistic learners? Overall, discussing the importance of problem-solving in mathematics classroom deepened my understanding of the mathematical processes that are outlined in the Ontario curriculum. It is clear that all of the mathematical processes, such as representing and communicating, are essential skills involved in mastering problem-solving skills in the mathematics classroom. Connecting these mathematical processes to problem-solving strategies will benefit me as an educator because I will ensure that I ask questions that evoke these mathematical processes for students so they can learn to the best of their abilities.
As an activity, we analyzed a question that related to finding the size of the square corners cut off of a box with an open top that would maximize volume. Throughout this activity, something I realized is that my style of problem-solving is extremely algebraic, and I am always looking for an equation or expression to solve a problem. Initially, I used calculus in conjunction with the use of the quadratic formula to determine the exact length of the square corners that needed to be cut out. Since this type of problem is a very 'traditional' problem that many calculus students see, I was ignorant to the fact that there are actually many other ways to approach this type of problem. After doing a gallery walk, the pictures below show other ways to solve this type of problem:
I had an 'ah-ha' moment when I realized that the gallery walk we did in class is actually effective in math classrooms, since we were using the gallery walk in practice and I found that I gained ample knowledge on how to use various problem-solving strategies to approach a problem. It was also interesting to detail that all three groups utilized three various approaches to this problem; which are algebraic, geometric and computational skills. I connected this to when my professor discussed the three methods to 'carry on the plan', and solve the problem. Overall, a take away message from this lesson is that problem-solving and inquiry-based learning strategies are more important than the tedious 'drill and kill' method to teaching mathematics. I noticed that this connected to the Bloom's taxonomy that we discuss in many of our assessment and evaluation courses. I invite you to a quick discussion question: Write a math question that is low on Bloom's taxonomy, and a math question that is high on Bloom's taxonomy. How do these question relate/differ?
References
Armstrong, P. (2018). Bloom's Taxonomy Center for Teaching. Retrieved from https://www.google.ca/search?q=blooms+taxonomy&rlz=1C1CHBF_enCA765CA766&source=lnms&tbm=isch&sa=X&ved=0ahUKEwiXvO2iz5veAhUqw1kKHXNaApcQ_AUIDigB&biw=1366&bih=657#imgrc=LY1ImA3IdOodNM:
Luminous Learning (2018). 8 Problem Solving Strategies for the Math Classroom. Retrieved from https://www.pinterest.ca/pin/571816483909896070/?lp=true
This week's lesson focused on the importance of instilling problem-solving skills in high school math students. We focused on the differentiation between various problem-solving strategies that were established by Polya and Doxiadis. Our class discussion regarding problem-solving strategies really evoked many practical aspects of the teaching profession. Personally, I felt like our discussion helped me in my tutoring with high school students. I sometimes feel that I am 'stuck in my ways' when it comes to teaching certain material. However, this class in specific has really challenged me to seek different ways in explaining specific math concepts to students. For example, techniques such as drawing a picture, or writing out lists of possibilities for a solution are strategies that I will implement into my own tutoring practice, and in my future classroom. Thinking Mathematically emphasizes the importance of students 'being stuck' and how problem-solving strategies will ultimately benefit them as students and help them through the 'being stuck' process, which is an important piece of the learning process (Mason, Burton & Stacey, 2010). Therefore, I feel like discussing problem-solving strategies is something I need to improve on as a professional. Attached is a brief list of problem-solving strategies that I found:
We also discussed how student attitudes are imperative when teaching problem-based learning strategies, and how using a three-part structured lesson plan can maximize problem-solving capabilities of students. A question that I have is how can I get students more engaged in the problem-solving process? Although strategies such as a gallery walk can be useful for some students, what other strategies can be implemented for those students who may learn in ways other than visually? What can we do as mathematics educators to be inclusive of logical, interpersonal and linguistic learners? Overall, discussing the importance of problem-solving in mathematics classroom deepened my understanding of the mathematical processes that are outlined in the Ontario curriculum. It is clear that all of the mathematical processes, such as representing and communicating, are essential skills involved in mastering problem-solving skills in the mathematics classroom. Connecting these mathematical processes to problem-solving strategies will benefit me as an educator because I will ensure that I ask questions that evoke these mathematical processes for students so they can learn to the best of their abilities.
As an activity, we analyzed a question that related to finding the size of the square corners cut off of a box with an open top that would maximize volume. Throughout this activity, something I realized is that my style of problem-solving is extremely algebraic, and I am always looking for an equation or expression to solve a problem. Initially, I used calculus in conjunction with the use of the quadratic formula to determine the exact length of the square corners that needed to be cut out. Since this type of problem is a very 'traditional' problem that many calculus students see, I was ignorant to the fact that there are actually many other ways to approach this type of problem. After doing a gallery walk, the pictures below show other ways to solve this type of problem:
I had an 'ah-ha' moment when I realized that the gallery walk we did in class is actually effective in math classrooms, since we were using the gallery walk in practice and I found that I gained ample knowledge on how to use various problem-solving strategies to approach a problem. It was also interesting to detail that all three groups utilized three various approaches to this problem; which are algebraic, geometric and computational skills. I connected this to when my professor discussed the three methods to 'carry on the plan', and solve the problem. Overall, a take away message from this lesson is that problem-solving and inquiry-based learning strategies are more important than the tedious 'drill and kill' method to teaching mathematics. I noticed that this connected to the Bloom's taxonomy that we discuss in many of our assessment and evaluation courses. I invite you to a quick discussion question: Write a math question that is low on Bloom's taxonomy, and a math question that is high on Bloom's taxonomy. How do these question relate/differ?
References
Armstrong, P. (2018). Bloom's Taxonomy Center for Teaching. Retrieved from https://www.google.ca/search?q=blooms+taxonomy&rlz=1C1CHBF_enCA765CA766&source=lnms&tbm=isch&sa=X&ved=0ahUKEwiXvO2iz5veAhUqw1kKHXNaApcQ_AUIDigB&biw=1366&bih=657#imgrc=LY1ImA3IdOodNM:
Luminous Learning (2018). 8 Problem Solving Strategies for the Math Classroom. Retrieved from https://www.pinterest.ca/pin/571816483909896070/?lp=true
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