When the students got to class, the first thing they did was pull out a book and started doing math strings. The teacher would write out any random multiplication problem, and the students would raise their hands when they had the answer. The teacher was making them up on the spot, as he had done all the ones from the textbook they are working off of. For anyone who does not know, a math string is a tool used to encourage mental math. The problem is started with one multiplication question, but really it could be addition, subtraction, division, any type, but in this case they did multiplication. They took the first set of numbers, and found the answer. Then moved to another question, this question usually featured one of the same numerators, for example, if the first problem was 2X2 =4, the second question could be 2X4= 8, then so on and so forth. It does not have to be done so neatly, as you could just to a number like 2X14= 28, which the students could use the previous "string" to determine using mental math. The other cool thing is when the teacher called on the students, they are automatically expected to explain how they got their answer. So all of the mental math strategies are being shared right there, on the spot. They are also apparently called "number strings". This blog had a lot of interesting explanations on number strings for younger students (grades 4-6). I researched through it a little and found that they use a more structured approach to their number strings, but the teacher I was working with had done so many that he did not need to pre-plan out his strings, he just worked through the numbers as he went.
Furthermore, I am interested and excited to see how the strategies I have been learning in math class will help me when it comes to my practicum. One of the concepts I enjoyed learning about was the "representation" concept. If students are comfortable seeing numbers as more than just numeric values, they can work with them in different ways. The example of 9 is the same as 10-1, or 8+1, or 3X3.
One of my "aha" moments this week was a lesson we did on inverting fractions. The idea that we just invert and multiply had come back to me during a required pre-assessment course. I had remembered what to do, and when to do it, but the "why?" stuck with me. Unfortunately for me, as a math student, no one had ever taken the time to explain why, it was always just well here is what you do, so now go do it. Being explained why was really awesome. So, for the inversion of fractions, I now understand that we do it so that we can compare unalike fractions in the same way. This video works to explain it better than I can, but the gist of it is that to compare fractions, they have to be "out of" the same thing, or else the comparison is meaningless.
One of the other things I was relieved to have learned about was that assessment for learning is not just a ranking of students, but rather a summation of their strengths and weaknesses, which are build around trying to help the students improve rather than to just judge them, slap a grade on a paper, and move on. With math, where simple yes or no right answers are available, this sometimes gets lost. I am thrilled to have the "good assessment plan" guide at my disposal now, because I think it will be really useful. It was also interesting to consider that when students do bad on an assessment, that teachers should reflect on that. Why did the student do poorly on the assignment/test? What could have been explained to them differently? What could I have done as an educator to ensure that these students succeed? I think these questions are all very important for us to ask ourselves every day, especially when our students are not understanding the concepts we are teaching.
I also really like the idea of instant feedback in seeing if students truly understand what they have just been taught. The use of Twitter or a face-paced multiple choice test could be options. Technology would be a great form of instant feedback, that could help struggling students who do not feel comfortable speaking up in class.
Overall, I feel I have made many strides this week, I really enjoyed reading Chapter 3 of "Making Math Meaningful to Canadian Students, K-8, third edition" in particular, because it discussed the pragmatic behind the sense work behind teaching such as the grading schemes and strategies in lesson planning. Each week, more of my math questions are being answered, and I am hopeful that in two years, I will be somewhat of an expert!
Another exciting thing we did in math class was students doing presentations. One of the students did a really cool presentation on multiplication, which was really engaging. I liked the assignments where we broke down the concepts and used them in practical ways. One of the presentations used number place values and we had to take certain numbers and use them in their correct place value using different combinations. This ended up being a really fun assignment, as we all raced to see what combinations we could come up with. These are the kinds of assignments I hope to include when I am an educator, because we all learned about place values while having fun. I definitely enjoyed the presentations! I think it will be great to continue seeing how my peers use various tools to teach math, and I am hoping to borrow some of those when I am an educator.
Citation
Small, M. (2013). Making Math Make Sense to Canadian Students K-8 (Third ed.). University of New Brunswick: Nelson Education.
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