In class this week however I realized that I didn't really understand why I was doing something.. I was just utilizing the algorithms I had been taught, I hadn't really rationalized things on a level that meant the learning was being deeply embedded. Fortunately there were many "ah-ha!" moments in class today especially when it came to working with negative integers.
The first activity we completed in class was a comparison of Teagan's height with a Giant's height based on their hand sizes.
The first thing we did was complete the problem individually then we moved on to comparing our methods as a small group and finally as a class. Well I had completed the question with ease and quickly too, I realized I was one of the few who had not immediately recognized that I could use a ratio to solve my problem... and my fixed mindset whispered "well you clearly don't get Math".. which is ridiculous! Because I did arrive at the answer, but I did it in a different way! I unknowingly was using ratios and decimals to get my answer! Hurrah for being creative in Math! That's what made this such a great problem, it was approachable and open to different approaches.
I'm glad we do so much discussion in our groups as I can gain insight about how else I can approach a problem and really understand how I get to an answer. How great are congresses??? This was one of my highlights for class today. Pat approached Nuha and I to help lead discussion to teach our group how another class had arrived at the unit price of each cat food can in Joel's problem and which algorithm they used to get to the answer.
This was such a great exercise. It was powerful to see how many different approaches our classmates had taken, there were so many different ways of thinking of the question that I hadn't realized! It also helped me to have to explain my thinking and then expand my understanding as I heard each group member's perspective.
The final "ah-ha!" moment occurred for me during Adam's lesson on integers. I had never given negative integers a story or a real life representation to better understand them. His comparison of negative integers to negative experiences gave them a context that was easy to relate to and remember! For example, if you have had 4 great experiences this morning then you have four levels of happiness! If I prevented two of the potentially negative experiences you would encounter that day [4 - (-2)] then I have increased your levels of happiness by two by being such a great friend! That's how I see it anyways... I'm excited to read what else my classmates learned from today!
Sarah, I loved that you felt the same way about this week as I did. I also found Adam's presentation on integers extremely beneficial in illustrating addition/subtraction of positive and negative numbers. I think this is a brilliant way to contextualize this concept for students and to 'de-bunk' the algorithms they are traditionally comfortable using = what do you mean when you add two things together the quantity decreases? The real-world applications he presented us with were useful for my understanding. I also took lots of stuff away from the Math congress and hope to be able to be organized enough in the classroom to be able to use this in the future!
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ReplyDeleteInterestingly enough, I found the set of "integer rules" we learned as students made it harder to remember them. Maybe it's just me but I get stuck when trying to remember 'strict' guidelines and therefore end up jumbling them or forgetting them altogether! I felt like a student during the Integer lesson today actually, rather than a teacher candidate since I really was relearning Integers! All the new strategies made me way more comfortable with integers then I had been before we entered class. I too talked about Adam's learning activity in my math blog this week! His explanation using real world examples was probably the most comprehensible thing (for me) that we learned today! And, it really reiterated what Pat keeps telling us about the importance of using the real world in our lessons.
ReplyDeleteHey Sarah, I'm glad you could relate to my presentation. One of the things I find interesting about all of our presentations is that everyone has been approaching their topic and lesson from a different angle which is giving us an opportunity to encounter so many different perspectives and ways of teaching math concepts. I think this will help to deepen our own understanding of the topics and give us great ideas to use in our own classrooms. Even when multiple presenters present on the same topic, everyone is adding their own unique twist. I think everyone has done a great job so far and I'm looking forward to learning from those that haven't gone yet.
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