Growth Mindset: A Student Guide To Success
Hi everyone, and welcome back to my blog!
Today's class focused on the mathematical processes involved in the Ontario math curriculum and connecting it to the ideology of a growth mindset, as opposed to a fixed mindset, in the classroom setting. We also briefly discussed the course content that is embedded in the curriculum documents to refresh our memory on what concepts are actually taught in the modern day high school classroom.
I felt very confident about the topics of mathematical processes and the Ontario curriculum because I have been tutoring high school math for years now. Doing the discussion about linear, quadratic, exponential, rational, trigonometric and polynomial functions made me reflect on all of my previous tutoring experiences. It also allowed me to connect the curriculum to the mathematical processes. It made me question, how would I help a student with their problem solving skills if I was tutoring a grade nine applied student, versus a grade twelve calculus student?
Then, the lessons focused shifted to establishing a growth mindset in your classroom versus a fixed mindset. A growth mindset is the idea that learning is infinite, and any concept can be learned if you keep trying and progressing as a learner. This was the concept that I really need to work on as a professional. I have always found math to be easy, and I used to believe that people were either good at math, or bad at math. This made me realize that I had more of a fixed mindset, which is a toxic characteristic to have in the teaching profession.
What really made me open my eyes was the TedTalk "How you can be good at math, and other surprising facts about learning" by Jo Boaler. Something that I learned from this video that surprised me was that when a student has a fixed mindset, their brain actually grows biologically and the synapses in their brains tend to fire faster, therefore being able to process information more efficiently. Something that intrigued me in the video is that they emphasize the importance of making mistakes when doing math problems. I have always said as a tutor that making mistakes will make you a better math student, because you can visually see what you did incorrectly, and apply the corrections and hopefully not make the same mistake again in the future. The focus of the video was when Boaler asked the audience the following question in the image below:
Initially, this question really made me reflect on the type of learner I am. As an mathematical and logical learner, I tend to reason with a more abstract approach to math problems. I used my knowledge of sequences and discrete functions to realize that the pattern for the nth case would be (n+1)^2. However, the video showed so many different approaches to solving this problem. And actually showed visuals on how people saw the shape growing. For example, some individuals used the 'Bowling Alley' method, where they noticed the bottom growing by two each time, where some people used the 'Rain Drop' method, where they saw extra blocks being dropped onto the old blocks. This reinforces the idea that there always in an alternate way to find a math solution, and through inquiry-based learning activities such as the one in the video, we can teach students to think in a more mathematical sense. Boaler's article titled "Mathematical Mindsets: Unleashing students' potential through creative math, inspiring messages, and innovative teaching" reinforces the TedTalk that Boaler presented. She discusses how inquiry-based learning in mathematics can reduce math anxiety within students who struggle with mathematics (Boaler, 2016). As a professional learner, I am going to challenge myself to explore different ways to solve problems that are more common-sense based, as opposed to always using abstract thinking to solve practical problems.
The next activity we did in class was the handshaking activity. As a class, we all had to get up and shake everyone's hand exactly once. I realized that this activity could be used for my own personal resource, as it is an inquiry-based activity that requires hands-on learning. These types of activities can be particularly useful for applied level and workplace level learners. We were then asked to determine the number of handshakes that occurred in the classroom. When we got up as a class to determine possible solutions to this problem, I went the combinatorics route to determine that there was 105 handshakes that took place. However, I saw so many other solutions in the classroom. Here are some examples:
The example on the left shows that Person 1 gives 14 handshakes, then Person 2 gives 13 handshakes, Person 3 gives 12, and so on and so forth. Then, adding up all the handshakes gives 105 handshakes. The example on the right shows that there are 15 groups of 7 handshakes, which also gives 105 handshakes. This was the part of the lesson I enjoyed the most, because I learned the most about different types of learners, and it reinforced the idea that inquiry-based learning will indeed be successful in math classrooms.
Overall, this lesson gave me ample opportunity to be reflective upon my own learning strategies, and be mindful of the different learning strategies that at might see in my own teaching profession. I also feel as if this lesson tackled the stigmas and stereotypes associated with individuals performing poorly in mathematics classes. This lesson allowed me to strengthen my own metacognitive practices as a professional, and I have gained so much insight on the growth mindset and I will incorporate these views into my own classroom.
Here is a video I found on YouTube. The video truly reinforces the idea that inquiry-based learning can make even the youngest of students understand the basics of an abstract concept like algebra. Thanks for reading my blog! Feel free to leave comments on my blog. Thanks!
References
Boaler, J. (2016). Mathematical Mindsets: unleashing students' potential through creative math, inspiring messages and innovative teaching.
Boaler, J. (2018). How you can be good at math and other surprising facts about learning. Retrieved from https://www.youtube.com/watch?v=3icoSeGqQtY&t=376s
Jorgensen, S. (2016). An Inquiry-Based Approach To Algebra. Retrieved from https://www.youtube.com/watch?v=5sgBZrEByKA
Today's class focused on the mathematical processes involved in the Ontario math curriculum and connecting it to the ideology of a growth mindset, as opposed to a fixed mindset, in the classroom setting. We also briefly discussed the course content that is embedded in the curriculum documents to refresh our memory on what concepts are actually taught in the modern day high school classroom.
I felt very confident about the topics of mathematical processes and the Ontario curriculum because I have been tutoring high school math for years now. Doing the discussion about linear, quadratic, exponential, rational, trigonometric and polynomial functions made me reflect on all of my previous tutoring experiences. It also allowed me to connect the curriculum to the mathematical processes. It made me question, how would I help a student with their problem solving skills if I was tutoring a grade nine applied student, versus a grade twelve calculus student?
Then, the lessons focused shifted to establishing a growth mindset in your classroom versus a fixed mindset. A growth mindset is the idea that learning is infinite, and any concept can be learned if you keep trying and progressing as a learner. This was the concept that I really need to work on as a professional. I have always found math to be easy, and I used to believe that people were either good at math, or bad at math. This made me realize that I had more of a fixed mindset, which is a toxic characteristic to have in the teaching profession.
What really made me open my eyes was the TedTalk "How you can be good at math, and other surprising facts about learning" by Jo Boaler. Something that I learned from this video that surprised me was that when a student has a fixed mindset, their brain actually grows biologically and the synapses in their brains tend to fire faster, therefore being able to process information more efficiently. Something that intrigued me in the video is that they emphasize the importance of making mistakes when doing math problems. I have always said as a tutor that making mistakes will make you a better math student, because you can visually see what you did incorrectly, and apply the corrections and hopefully not make the same mistake again in the future. The focus of the video was when Boaler asked the audience the following question in the image below:
Initially, this question really made me reflect on the type of learner I am. As an mathematical and logical learner, I tend to reason with a more abstract approach to math problems. I used my knowledge of sequences and discrete functions to realize that the pattern for the nth case would be (n+1)^2. However, the video showed so many different approaches to solving this problem. And actually showed visuals on how people saw the shape growing. For example, some individuals used the 'Bowling Alley' method, where they noticed the bottom growing by two each time, where some people used the 'Rain Drop' method, where they saw extra blocks being dropped onto the old blocks. This reinforces the idea that there always in an alternate way to find a math solution, and through inquiry-based learning activities such as the one in the video, we can teach students to think in a more mathematical sense. Boaler's article titled "Mathematical Mindsets: Unleashing students' potential through creative math, inspiring messages, and innovative teaching" reinforces the TedTalk that Boaler presented. She discusses how inquiry-based learning in mathematics can reduce math anxiety within students who struggle with mathematics (Boaler, 2016). As a professional learner, I am going to challenge myself to explore different ways to solve problems that are more common-sense based, as opposed to always using abstract thinking to solve practical problems.
The next activity we did in class was the handshaking activity. As a class, we all had to get up and shake everyone's hand exactly once. I realized that this activity could be used for my own personal resource, as it is an inquiry-based activity that requires hands-on learning. These types of activities can be particularly useful for applied level and workplace level learners. We were then asked to determine the number of handshakes that occurred in the classroom. When we got up as a class to determine possible solutions to this problem, I went the combinatorics route to determine that there was 105 handshakes that took place. However, I saw so many other solutions in the classroom. Here are some examples:
Overall, this lesson gave me ample opportunity to be reflective upon my own learning strategies, and be mindful of the different learning strategies that at might see in my own teaching profession. I also feel as if this lesson tackled the stigmas and stereotypes associated with individuals performing poorly in mathematics classes. This lesson allowed me to strengthen my own metacognitive practices as a professional, and I have gained so much insight on the growth mindset and I will incorporate these views into my own classroom.
Here is a video I found on YouTube. The video truly reinforces the idea that inquiry-based learning can make even the youngest of students understand the basics of an abstract concept like algebra. Thanks for reading my blog! Feel free to leave comments on my blog. Thanks!
References
Boaler, J. (2016). Mathematical Mindsets: unleashing students' potential through creative math, inspiring messages and innovative teaching.
Boaler, J. (2018). How you can be good at math and other surprising facts about learning. Retrieved from https://www.youtube.com/watch?v=3icoSeGqQtY&t=376s
Jorgensen, S. (2016). An Inquiry-Based Approach To Algebra. Retrieved from https://www.youtube.com/watch?v=5sgBZrEByKA
Hey Jarrett!
ReplyDeleteI used to tutor grade 9 and 10 math a lot and I recall the difficulty I went through trying to find numerous ways to teach a certain problem to a student and finding a new way different than how I learned it. I believe keeping updated on your resources and using other teacher’s opinions and asking for help will allow you to find ways in tutoring a grade 9 vs. a grade 12. I also believe I need to work on promoting positive growth mindset also, math came natural to me and I never considered others in my classes at the time struggling when I was in high school. I believe showing ted talks or YouTube videos in your future classroom will be able to raise awareness of a positive growth mindset amongst your students and also reinforce that it is okay to get the answer wrong and to just try again. I also was intrigued by the same math problem of “How do you see the shapes growing.” I think it would be super interesting to incorporate such problems in our future classrooms and it will help us as teachers to identify how our students think about said problem. I appreciate you sharing a video that reinforces the idea of inquiry-based learning. Great Post! Cannot wait to continue to read your blog.
All the best,
Nicole
Hi Jarrett!
ReplyDeleteI also agree that the TED talk video opened my eyes about the different ways one question can be interpreted! It is important to keep in mind that the teacher's way of thinking is not the only way to solve a question and allowing students to venture out with different tactics to visualize a problem without any academic penalites are a crucial factor of letting students grow out of their fear of math.
I believe that many students are reluctant to try new ways of solving problems purely due to their fear of failing or looking silly, which can be very detrimental to the student's self-esteem and growth. I also found the handshaking activity to be a great way of engaging students and allowing students to get involved with the question without actually asking the question beforehand.
Thank you for the post!
-Michelle
Hey Jarrett, thanks for your intriguing post! I have also been a high school math tutor for a few years and have found that promoting a positive mindset in failure is one of the most difficult things to accomplish as a teacher. When a student (especially young students) get a question wrong, they are more likely to feel depleted than to find solace in the fact that they have room to improve. Promoting the idea of an imperfect philosophy (the idea that no matter how brilliant we are, there is always room to improve) is a critically important approach in my opinion. I have found that good ways to generate growth mindsets out of students who are struggling is to create relatability. Talking to students about your own stories of academic struggle (we all have them) is a great place to start to create that relatability. Students often can relate to their tutor because they can see in them a role model for where they would like to see themselves. If we as teachers can show students that we are more similar than different, it may help initiate a strong growth mindset that will help the student best handle their academic (and life) struggles. Thanks again Jarrett!
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