Manipulatives

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Many students remember using manipulatives like patterning blocks, clocks, counters, or base ten blocks in elementary school. However, manipulatives can be used and add great value to high school math lessons too!

In class we watched a video clip from a math conference where Dr. Ruth Beatty discussed manipulatives and multiple representations in mathematics. Dr. Beatty made an interesting point regarding the stigma attached to using manipulatives.

Furthermore, our course instructor Liisa Suurtamm, talked about who should use manipulatives. It was stated that manipulatives in a math lesson can be used for all students, not just students who are struggling to understand the concept being taught.

Together, this made me really question what I thought the purpose of manipulatives was. My previous understanding of manipulatives was that they were to help students who couldn’t understand an abstract way of looking at a math concept. By involving all students in the use of manipulatives, the stigma around certain students using manipulatives is addressed.

In this article, Marilyn Curtain-Phillips states that manipulatives are the missing link in high school math. She argues that “Manipulatives are value resources for accelerating and deepening students understanding of math”, which supports exactly the ideas discussed in class. By using manipulatives, both students who may be struggling to understand a concept and those needing a way to further their understanding can benefit.

Liisa Suurtamm, EDBE 8F83 Lecture 3: Conceptual 

and Procedural Understanding, Retrieved from online lecture notes. 

We did a couple different patterning examples as a class that challenged my way of solving a problem. We were given a pattern like the one here and asked to describe what position 4 would be and what the pattern was. 

For me, it would have been much quicker to write out a table and find the pattern that way. And although there is nothing wrong with that, I tried to look at the problem in terms of the patterning blocks and answer the question using a different type of representation then what I am used to.

What will I take with me from this lesson? That there are so many interesting ways to incorporate manipulatives into a high school math class and these can help a range of students, not just students who may be struggling. Multiple representations of concepts are important to teach and to recognize that students may see things in a wide range of ways. I hope to further my exploration with incorporating manipulatives into my lessons during my practice teaching blocks this year. 

Week 2: Verbs, Estimation & Would You Rather...

This weeks focus was on learning about the Ontario Math curriculum. One topic that I found particularly interesting in this class was the focus on verbs! Going through the curriculum documents, we identified the verbs that were included in the specific expectations, indicating to us as teachers how our students should be engaged and involved in the learning.

Some of the more common verbs included were: determine, solve and simplify. All of these make sense for a math class.

The ones that I found most interesting to be included were the ones that I do not immediately associate with math. For example: create, construct, illustrate, and develop. My memories of high school math classes definitely do not involve a lot of creating, constructing, illustrating or developing but I am excited to be able to change that for my future students.  Adding more “doing” into our math lessons provides engagement for students.

http://www.myastrologybook.com/Pythagoras-proof-Pythagorean-Theorem.htm 

Why is this something important to remember as a teacher candidate? As stated in class, it is easy to look at the curriculum documents and teach to the topic addressed in the expectations. However, as teachers, it will be important to recognize that verb too! For example, grade 9 applied math states to  “relate the geometric representation of the Pythagorean theorem to the algebraic representation. That is much more than an indication to start a lesson on the board about Pythagorean theorem.

Another topic discussed in class was estimation. Estimation can be a difficult topic for some students to see the value of. 

Why is estimation important to teach in the math classroom? Without estimation student’s will not know if their answer is reasonable.  I found this article on teaching estimate and accuracy to interesting and supports the idea of teaching estimation. 

I will end this post off with a Would You Rather... math problem. We did this style of question last week and I thought it was a great idea to incorporate into the classroom. 

Would you rather...

Have a million dollars now or a penny doubled every day for 30 days? 

The answer, along with some different methods to solving this problem can be found here.