Happy New Year and welcome back to the Alge-blog! This is my first blog of the second semester, and I am excited to get into it! Unlike last semester, we are starting the first few weeks by participating in professional reading, where each group member is responsible for certain roles in analyzing and sharing information on textbook chapters. This week, I was the illuminator, which required me to draw an image or graphic organizer relating to chapter 1.
What stood out and what I learned
During our group discussion, we talked about the importance of group work and exploration in a math classroom. This allows students the opportunity to have agency over their own learning and identify patterns themselves before being introduced to hard rules and formulas. This strategy allows students to gain a deeper understanding of why a problem is solved in a certain way.
- Specializing: Using specific examples to try to figure out a problem
- Generalizing: Moving from specific examples to a general rule or pattern
Specializing in an important thinking process that should be encouraged within a math classroom because it allows students to start feeling out a problem, get familiar with it, and identify any patterns they notice. Specializing can help make a generalization clearer, leading to a deeper understanding of general rules.
We also highlighted the importance of getting stuck. In school, often students see getting stuck as a failure, and will often give up, claiming “I just don't get it,” or “I’m not good at math.” As a future educator, I think we must work to shift this mindset and encourage students that getting stuck creates a valuable learning opportunity. Struggling can be productive, where meaningful thinking occurs, so teachers need to take advantage of this and shift the focus from the product and memorization to the process and thinking skills.
Specializing and generalizing are connected, and one can start from either side. If given a general statement or rule, it can be tested using specialization to test or build understanding. Alternatively, some may start by specializing and notice trends, then use these identified patterns to create generalized statements.
We tested this in class using this prompt:
Imagine a long thin strip of paper stretched out in front of you, left to right. Imagine taking the ends in your hands and placing the right hand end on top of the left. Now press the strip flat so that it is folded in half and has a crease. Repeat the whole operation on the new strip two more times. How many creases are there? How many creases will there be if the operation is repeated 10 times in total?
In our group, we started to break down the problem by folding a piece of paper in front of us. From this, we were able to identify the number of creases for 1, 2, and 3 folds, but it got more challenging when we got to 4. From this, we noticed the amount of increase doubles each time. This strategy uses specialization, where we are testing the first few specific examples, noticing patterns, and then creating a generalized statement.
The Ted Talk by Jo Boaler was very interesting to me because she talked about the myth of the “math brain”, and that one is either born with it or not. She highlighted that mistakes are a good thing, and they actually encourage learning, and the brain grows. Mindset is such a vital element when it comes to learning and development. Those with a growth mindset believe that they can do something, learn more, even when they fail. A fixed mindset stunts learning and keeps the brain from growing from mistakes. She highlighted that educators need to prioritize shifting the mindsets of students, which reinforces the ideas I described in our group discussion above.
She used an example of a pattern, similar to what we solved above using the paper, which required analyzing a pattern. She encouraged us to think about the pattern visually, not just numerically, and the various ways that people in my class, and in the video, described how they saw the pattern surprised me. Some of the methods brought to light I never would have thought of, like imagining a layer of snow falling over the pile and adding another layer. This emphasizes the need for teachers to be open-minded and understand that students approach and think about problems differently, sometimes even in ways that they wouldn’t even think about themselves. This does not mean a student is wrong for thinking a certain way; it is just different.
Key Takeaways
This week's lesson highlights the importance of encouraging a growth mindset in students and helping them to achieve their full potential. All students have the ability to succeed in math, as it isn’t a skill that one is born with. I will apply the following strategies in my future classroom to help meet this goal:
Encourage group discussion and collaboration in problem-solving so students can share different perspectives and learn from each other, shifting to a student-centred learning environment.
Emphasize specialization when it comes to problem-solving. Allow students the opportunity to explore concepts, identify patterns, and analyse their findings.
Encourage students to see mistakes as learning opportunities by using positive and encouraging language.
Shift away from right-or-wrong questions to more open-ended questions, allowing for multiple solutions, as students may analyze, visualize, and understand questions differently.
I want to create a classroom environment that is supportive and encouraging, allowing students to make mistakes and learn from their failures. I want students to become more confident in their skills and steer away from the “I am just not good at math” mindset. As a tutor, one of my favourite things is knowing I made a positive difference in a student's life and helped them to build their confidence. I look forward to being able to do that in my future classroom and creating a space that allows students to explore and have fun with math.
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