Math Reflection Week 6: Technology and Real Life

For class this week we focused on the use of technology in the classroom and how it can facilitate blended learning and differentiated instruction. My table group focused on the SAMR Model of using technology in the classroom. The SAMR Model divides technology use into four parts: substitution, augmentation, modification, and redefinition. Substitution involves using technology as a substitution with no functional change, while augmentation is a substitution with a functional improvement. Modification allows for technology that significantly redesigns the task, while redefinition allows for the creation of new tasks previously impossible. As teachers for 21st century learners we must strive to design tasks that best use modifications and redefinition of technology for learning.

Michael Feagan. (Oct.19 2017). SAMR Model [photo].

  The online activity that I did for this week involved watching a video about math in real life. I thought this topic would be the most interesting as children learning math often say things along the lines of "There's no real life application for learning math" or any other specific math topic. I like this video because at its core it highlights that the real world skill we want students to walk away with by learning math is pattern recognition. One of the most famous mathematical patterns that this video uses as an example is the Fibonacci spiral. The video highlights all the real world uses of the spiral both in nature and man-made things. This helps show students that mathematical patterns are present in all natural and unnatural creations in their everyday lives. In the end making student curious about mathematical concepts is key but giving them the big ideas (as discussed in last week's blog post) like pattern recognition helps them be curious math investigators.

Math Reflection Week 5: Big Ideas or Memorization

Although we didn't have an in person class this week we still had plenty of online activities to do. The one idea that stuck out to me, and the one that I will be spending the majority of my post focusing on, is the concept of big math ideas versus memorization of math formulas and procedures. For me this debate was sparked by a short video you can watch below.

Dr. Boaler argues that there are few general math principles that students need to understand. Students often struggle with math because they get caught up in memorizing details and procedures. With this kind of approach math is less about how many questions you can get right, and more about the knowledge and understanding that go behind the mathematical solutions you arrive at. Principles such as student intuition, making sense, and finding ways to represent problems can all contribute to a student's understanding of the big ideas.

Although I do agree with all of the basic concepts represented in this video there are some structural problems with how I feel this is implemented in an education system. Firstly I feel like this outlook, that knowing big ideas about math, is less testable. At least in the old fashion sense of math tests filling in multiple choice responses. As that method does not allow the student to show their thought process and their knowledge and understanding of wider math ideas.

It should not come to any student teacher's surprise that Ontario students are struggling in math, according to EQAO testing. With only half of grade 6 students meeting the provincial standard in math. This is very worrying, and it does not surprise me that Ontario boards are starting to emphasize math competencies more in students and educators. However, I wonder if teaching students big math ideas are really assisting them in math, according to EQAO it might not be.This is not to say that it is a bad idea, but that EQAO might be ill equipped to assess this kind of knowledge from students.

Math Reflection Week 4: Rich Tasks and Number Flexibility

This week in our math class we focused on participating in and assessing rich learning tasks in math. A rich tasks boils down to one that is: essential, authentic, engaging, and active. One such task that we performed in class was a problem involving counting the fingers on a hand. The basic problem was that if you started counting your fingers starting with your thumb, index, middle, ring, pinky, ring, middle, index, thumb, index, etc. what finger will you land on when you count your 10,000 finger? Everyone came up with different ways of solving this question but the one that I found most interesting was the one Mina shared with the class. It was a video of how someone else solved the problem by thinking of it as an eight fingered hand rather than just one five fingered hand.

Michael Feagan. (Sept.29 2017). Hand Problem [photo].

I think that all of the different ways students had to express this problem help support that this is a rich learning activity.

The final thing I did this week was watch the math mindset video on number flexibility. The exercise the video wanted us to do was to do 18x5 in our heads. I did this by knowing that if 10x10 was 100 then 5x10 would be 50 and 5x8 is 40, so 50+40 is 90. Perhaps a longer way of doing it, but I would not be surprised if I had many students in my math classes who would mentally answer this question this way. This exercise is pretty similar to doing math strings, which I think are an excellent way of bettering number flexibility.

Math strings I think are an excellent way to better a student's mental math flexibility. Recently I presented a webinar with my classmate Paula that highlights the benefits of doing math strings, you can see it in the video below.