Problem Solving: A Complex Task

Colourbox. (2018). Retrieved from https://www.colourbox.com/image/problem-solving-word-cloud-concept-9-image-

Hey everyone! Welcome to Blog Post #3

          In today’s class we unfolded many important concepts around problem solving strategies and mathematical processes such as communicating, selecting tools and computational strategies. The challenging part of today’s class was being able to go from a student’s perspective and move to a teacher’s perspective and figure out how to unpack different ways to teach math. One part that really struck me was the endless amounts of examples of mathematical problems teachers have to solve. For example, I find it hard in our classes to make lesson plans for math classes without being in practice. I struggle a lot with differentiated learning ideas without knowing the students personally. Therefore, once I get into practice I will be able to relate to all of these problems on a greater level. Teaching math in itself is like problem solving as we are continually building new mathematical knowledge on a daily basis and applying and adapting a variety of appropriate strategies to solve problems (Lecture 5, Oct. 2018). 

          Additionally, today in class I began to wonder how I will as a future mathematical educator teach my students how to problem solve. I think a way is to use anchor charts as guides for students to use when going through problem solving questions. The image below examines a useful way to integrate effective problem solving into your classroom. Growing up I struggled with some areas of math especially when it had to do with problem solving. An author we discussed in class was Deborah Loewenberg Ball and “Uncovering the special mathematical work of teaching.” This article unfolded complex topics such as “interactive mathematical work of teaching” (Ball, 2017, p. 1). Students today have a negative mind set towards mathematics, because they believe that they cannot problem solve. Therefore, it is important to identify differences in teachers’ and students’ views about problem solving to help develop a greater understanding about the challenges they may be facing to work towards achieving their goals (Ball, 2017). Teaching is a co-constructed process and it is important to use your other colleagues as resources and work together to build lessons and activities that relate to the students. It is also important to talk to other departments such as the science department to align important skills with one another so the skills the students learn in math can be transferred to science. 

C.H.A.S.E. - Math Problem Solving Strategy. (2018). Retrieved from https://www.teacherspayteachers.com/Product/CHASE-Math-Problem-Solving-Strategy-2277988

           An interesting activity we did in class was the “Open Box Problem.” The problem can be found below, along with the answer to the problem from my classmates in the photos below.

An open box, without a top, is to be formed from a 9 x 12-inch piece of cardboard by cutting off
square corners of equal size and folding up the edges.

a)      What should be the size of the square corners cut off in order to obtain a box of maximum volume?

b)      Show 2 different solutions.  You might use a numerical, pictorial, graphic, and/or algebraic model.

          We all split into groups and came up with 2 different solutions to the problem. We then walked around in our groups to look at the work of our classmates. This strategy is called the Gallery Walk. This method is similar to a museum, the class then travel around and view other students solutions. The students then reflect and observe on what they are viewing. This is an activity I would use in my future classroom. We spoke about the difference of solving a problem horizontally vs. vertically. I believe when you sit down at a desk (horizontally) there is less energy and focus compared to standing up and using the whiteboard (vertically) as the platform for discussion and solving the problem. It also allowed us to get on our feet and include more verbal communication then sitting down and looking at our desks. It was also interesting to get a grasp on how other students in the classroom solved the same problem giving us as educators a different view point on how to solve one problem, in many different ways. This is an excellent way to develop a greater understanding of how your students solve problems and I believe problem solving in groups helps develop critical thinkers and increases students’ collaboration skills. This may also allow for students to explain their own thinking out loud to the class and this can help with the students’ presentation and oral communication skills.

Thank you for reading my blog! See you next time!

References

Ball, D. (2017). Uncovering the Special Mathematical Work of Teaching. University of Michigan, Ann Arbor,  USA. DOI  10.1007/978-3-319-62597-3_2. Pg. 1-24.