Week 18 - Calculus and Vectors

This week we were introduced to activities and teaching strategies that would be beneficial in a calculus and vectors course. Being the final math course offered, it can be daunting to teach and, in the case of the students, learn. This being said, the teaching strategy for teaching chain rule made teaching and learning simpler and more enjoyable. Lots of students struggle with chain rule, especially when there are multiple terms to differentiate with chain rule. This strategy uses shoe boxes and plastic fruit to illustrate the order of events for chain rule.

This strategy, and other visual strategies that help to illustrate abstract mathematical concepts are beneficial  to any and all math courses. They demonstrate how these concepts work and the use of these strategies help to make the entire experience more memorable. The chain rule is still fresh in my mind a couple of days after the strategy was presented. I wish I had this strategy shown to me in high school; it would have made it easier to remember how the order went in advanced questions in high school and university.

Some students might be skeptical at first as to how it relates to mathematics, but in the long run it would be better for our students to use visual/kinesthetic representations for learning. I hope to use this strategy, among many others, when I teach mathematics this next teaching block, and whenever I am fortunate enough to be placed in a math classroom.

Week 16 - Grade 12 Advanced Functions

I didn't fully understand logarithms until I was in post-secondary. It was only touched on briefly in my advanced functions class because there was a lot of other concepts in the curriculum that needed to be addressed. So during this class when the log loop was introduced, I was quite intrigued. A helpful hint such as that for inverting logarithms would be incredibly handy for the advanced functions class, and any other class that uses logarithms. The "log war" game introduced after the log loop is also a great way to get students to practice inverting logarithms without it seeming like work that they have to do. Our group soon came up with tricks to find out which logarithm is the biggest by seeing which ones would be negative, 0, or positive.Our group was highly energized (maybe it was the cookies that were handed out just before) and motivated to find out who was the winner for each round.

Games like log war help to make math class and learning more fun for the students, which can help them to retain information better. They don't feel that they have to do the work because the game helps them to want to do the work, and they are still fulfilling the curriculum requirements. I know I have said this before, but when I have a math class, or any class for that matter, I would like to try to incorporate games as much as possible with the curriculum because I believe that the students learn best when they are motivated to learn and games, such as log war, help to increase student motivation. They are a great tool for student learning.

Week 15 - Grade 11 College Math

This week we had the opportunity to see math, specifically mean, median, and mode, transformed into a game. I found the game to be an interesting look on this specific math concept that is usually seen to be more of a tedious activity instead of the fun game that it was. In groups we were competing to see who could get the highest average over 3 rounds of drawing cards from the deck. A little bit of healthy competition can make any work more enjoyable for students because it gives the students a reason to do the work.

This activity lets the teacher know that the students know what they are doing, while letting the students have fun in the classroom. It can also be modified for median and mode as well if there is extra time. This activity and the use of cards can also be modified for graphing. pick out cards and graph their numbers as you pick each card. Then the students would find the slope height(s) of their line(s). Giving something ordinary (like math) even a little bit of a twist can make learning more interesting for the students and there would be a higher chance of their knowledge staying with them for longer. For example, one of the few things that I still remember from grade 10 math was when the teacher brought in a wii fit; we each took a turn playing ski jump and took the first half of the graph of our jump and had to recreate the second half of the parabola. The task could have easily been menial, but the teacher took extra initiative to make the activity fun for us and that made it a memorable experience. When I have a math classroom, I would like to try to have a fun activity to go along with each unit to make the students' learning more memorable.

Week 14 - Grade 11 Functions and Applications

I was intrigued for this week's class because I was curious to see how close the mixed course would be to the university course. In high school I only took the university level courses so this year I have been interested in looking at the other courses in order to get a more rounded view of the math curriculum. The graphing activity was particularly interesting because it physically involved the students in their own learning. This activity is a good assessment as learning activity because the students are able to see what they are doing right and what needs to be improved right away and are given the chance to correct their mistakes.

Even though this activity is geared towards the mixed course, I believe it would also be useful in the university course. The more the students are involved in their own learning, the more they learn. This activity challenges the students' knowledge of domain and range through graphical representations of data. Student involvement in learning also helps with creating a growth mindset in the classroom. This activity shows the students that it is okay to make mistakes because we can correct them and learn from them. I believe students learn more from making a mistake than they do from getting it right the first time. When I have a math classroom (hopefully) I would like to involve the students as much as possible in their own learning.

Week 13 - Grade 11 Functions

Each lesson presented this week for the grade 11 functions class used visual aids to implement understanding for students. My particular favourite was the matching games used for trig identities. Saying 'trig identities' is usually enough to make a room full of people groan, however the matching games used in this lesson plan motivated us to dive into proving the identities given. Below is a photo of each matching game that was used.

The matching square has a higher difficulty level since each side of each small square has to be equal to it's adjacent square, however it would be a good 'exit card' activity, depending on your class. It could also be used as an extra activity for the students who are ahead of the class. The essence of matching activities can be used for more than just trig identities and I feel that they would be an asset to the math learning environment. Students are more likely to be motivated to finish a matching activity than they would be to finish the exact same work on a worksheet. Plus, the students would still be working their way through the curriculum requirements. Class doesn't have to be boring, just because it's math; I think that the best learning happens when students are having fun with the learning because the learning is more memorable and is more likely to stick with them even after exams are done.

Week 12 - Efficacy

Student and teacher efficacy is a term that I didn't really understand before watching Professor Cathy Bruce's video. While watching this video I found that it is greatly linked with the growth mindset that we talked about earlier in the year. Students and teachers with a growth mindset would have high student and teacher efficacy and would be more willing to take on new tasks without the fear of failure. On the opposite side, students and teachers with a fixed mindset would have low student and teacher efficacy.

As the video said, teachers with high efficacy are more willing to try new activities with their students and will also try harder to help their students learn because they have higher success standards for themselves as well as their students. I believe that having high teacher efficacy is essential in modern classrooms. Students will raise their own learning standards if their teacher's standards for them are raised, compared to when their teacher's standards for them are lower. When there is high teacher efficacy in the classroom there is a better chance that students with low efficacy can raise their efficacy levels and improve their learning habits. Similarly to teachers with growth mindsets being able to change their students' fixed mindsets to growth mindsets. Trying different methods and different tools to teach math concepts will help reach more of the students' learning abilities. Teachers with high efficacy would be more willing to use these differentiated learning techniques, which would help them to have a higher student success level.

I hope that when I become a teacher I would have a growth mindset and a high enough teacher efficacy level to help my students improve their student efficacy levels and to not only learn what is being taught, but understand it as well.

Week 11 - Grade 9

This week in class we had two lessons geared towards a grade 9 classroom; one for academic and one for applied. Even though they were two different lessons for two different streams, they both used visual aids to make the math more concrete. I really liked the visual representation of the math concept for the academic class; representing the pattern between polygons and the sum of the interior angles. Starting the lesson off, we were instructed to divide the polygons into triangles, where each line had to start from the same point. Using previous knowledge the students can then tell us the sum of the interior angles by adding up the sum of all the angles of each triangle in the polygon.

 

 

I didn't know this relationship between the number of triangles that fit into the polygons and the sum of the interior angles of regular polygons before this class and the lesson made this relationship apparent. I was able to see, first hand, how the use of visual representations can make math concepts easier to understand as well as more memorable later on and I am now even more intent on creating opportunities while teaching for visual representations for every stream.