EDBE 8P54 Math Blog

Math Blog Week 6

            Throughout these six weeks it is very interesting to go back and look at the development of learning. When looking at my week 1 blog post through to my week 5 blog post there is so much more evidence about mathematical concepts then when we first started. To be honest, this course was not what I expected. I expected to learn more about the mathematics part of teaching. What I did not expect to learn is the pedagogical side of teaching math. Concepts that seem so simple but can make such a huge difference on students’ success in math. However, to get to these concepts we first had to get passed the stigma behind math.

            The first thing we did in the course was to erase the stigma that some people are bad at math and some people are good at math. This is absolutely not the case. Some students just need a little more time than other students, some students just need to be taught in different ways. Many students need more time to learn math than others, but school moves on so quickly, that those students do not get a chance to excel and end up falling behind in math. This is where the math divide begins. Another hinderance to teaching the math curriculum is that so many students are frightened or embarrassed to make mistakes when doing math. These students need to be aware that mistakes are what help us learn and help our brain grow and it is our job as teachers to encourage this growth. If all students valued being hard workers over being "smart" I believe there would be more students achieving success in every subject because they would be more willing to challenge themselves instead of scared to embarrass themselves by not fitting the ideals of being “smart.” Once this base is built, students can move on to truly succeeding in math.

            Now that students have an understanding that making mistakes and trying new things is how students learn, they can now be more confident in doing math in many different ways. Math can be done in so many different ways and some students are more comfortable learning one way more than another. When students understand that everyone learns differently they are more comfortable showing the rest of their class how they learn best instead of focusing how their way is not the same as someone else’s way.

            The week after, we discussed some struggles and misconceptions that students may have in math. When students are already comfortable with idea that making mistakes is a good thing to help them learn better in math, it is easier to help them get over their struggles and misconceptions. One of these misconceptions that we talked about as a class is how students view the equal sign. We also talked about how eradicating these misconceptions is much easier through visuals and manipulatives. Like, previously stated, students learn in all different ways and to help them learn it is best to teach in many ways too. Using oral explanations, written work, visuals, manipulatives, and other forms of differentiated instruction, hopefully all students’ mathematical needs can be met. When teaching students math, they tend to have numerous misconceptions that need to be untrained. As teachers we need to find the best, most kid-friendly way to achieve this and end the confusion and bring forth clarity.

            Helping students get past their misconceptions and struggles is all part of the learning process. To wrap the 6 weeks of this course up, we watched a video to analyse the learning process of a student working through a problem while a teacher observed and asked probing questions. It was quite valuable to watch this video as we learned so many different things just from watching, what seems like, a simple learning process. Simple and open-ended questions asked at the right moment can make all the difference in students’ learning. We also learned that gesturing through a learning process is very important in students’ learning process. We learned that research shows that when teaching, gestures help students better understand. On the other hand, we also learned that when students gesture it also helps them better problem solve and understand their own thinking. As much as gestures and prompting questions are of value, we also learned that as a teacher, you must honour your students’ learning process. We must give them time to try to figure it out, because more times than not, they will end up figuring it out.

            Throughout the 6 weeks I have learned to value the learning process and have learned simple ways to enhance it and allow students to work on their growth mindset and succeed in math whether they thought they were “good” or “bad” at math. Each student has the potential to grow and be confident and competent in math.

Math Blog Week 5

This week we learned about the learning process while watching a video of a girl trying to solve a patterning math problem with tiles. During the process the lady prompted the girl to explain her thinking as best as she could. The teacher also asked the student questions to prompt higher and critical thinking from the student.

            It was quite valuable to watch this video as we learned so many different things just from watching, what seems like, a simple learning process. For example, we learned about prompting questions. Simple and open-ended questions asked at the right moment can make all the difference in students’ learning. When the student in the video was asked prompting questions at the right time it allowed her to take her learning to the next level and reach a higher level of critical thinking. Also, when the teacher had noticed that the student was wrong or making a mistake, the teacher would ask the student something about why she did what she did. This question drew the student’s attention back to that area of the problem and also prompted her to think about why she did what she did that way. Again, this simple question allowed the student to question her own thinking, making her aware that she made a mistake and allowed her to fix it. All this was accomplished and not once did the teacher mention that the student might have made a mistake.        

            We also learned the value of gesturing during the learning process. We learned that research shows that when teaching, gestures help students better understand. On the other hand, we also learned that when students gesture it also helps them better problem solve and understand their own thinking. An example of this in the video is when the student visually corrected her tiles. She was gesturing while speaking and even though her words were not correct, her gestures were. As much as gestures and prompting questions are of value, we also learned that as a teacher, you must honour your students’ learning process. We must give them time to try to figure it out, because more times than not, they will end up figuring it out.

            The last thing we learned from the video is that students must be taught to look ahead in their problem solving and not just told to think recursively, a mistake that many teachers make, especially in patterning. When students can look ahead in their problem solving, it shows that they truly understand the process required to solve the problem. Getting students to practice thinking ahead instead of recursively also helps them train their brain to logically and critically think.

Overall, it was quite interesting to watch the learning process of problem solving.

Math Blog Week 4

This week we discussed some struggles and misconceptions students have with math. One topic we discussed that students often have trouble comprehending is the true meaning of the equal sign. The other concept we discussed briefly that students have trouble understanding is the subject of algebra. What usually confuses students is that they struggle with numbers and then they finally get comfortable working with numbers in mathematics and then letters are introduced to confuse them all over again. However, this week in class I noticed some strategies to help eradicate these misconceptions that students have.

            When we were discussing the misconception of the equal sign, we discussed making sure students are aware that the equal sign means that one side equals the other and not let them get into the bad habit of thinking that the equal sign means “the answer is.” One way that students can see that an equal sign represents that one side equals the other is to expand numbers to visually show students that these numbers on the left side equal the numbers on the right side. Another very visual way to show students the balancing effect of the equal sign is to use the visual representation with a scale. You can use a scale drawn on the board underneath the numbers to represent the equal sign or if you can, you could bring in a physical scale to provide your students with manipulatives to kinaesthetically represent the equal sign.

            Then we did the animal problem, the problem that used animals to represent numbers to get to an end value. When we were doing this activity, I thought that this would be a great way to help students understand that the letters represent an unknown variable, or in child-friendly language, an unknown number, that completes the equation. At first, we could use pictures like a frog in the place of the unknown variable instead of letter to get students used to the idea of finding unknown variables. Then when students are confident in this method, introduce letters to represent unknown variables instead.

            When teaching students math, they tend to have numerous misconceptions that need to be untrained. As teachers we need to find the best, most kid-friendly way to achieve this and end the confusion and bring forth clarity.

Math Blog Week 3

This week in math class we were given the opportunity to complete math problems. We were instructed to attempt to find more than one way to complete the math equation which I personally believe was a good and challenging exercise for us because we are so used to completing math problems in a very structured and specific way. It was quite a struggle to come up with a different way to solve the problem at first because we are so rooted in our traditional ways of thinking. Afterwards we were able to do a gallery walk to see how other partners may have solved the problem. I appreciated this because I was able to see different ways that the problem could be solved. The way the others solved it was not immediately explicit at first glance and we had to challenge ourselves again to deconstruct their problem solving to see how they achieved the answer.

Next, we worked on multiplication tables in a group. Half of the class were playing the part of the students and the other half of the class was allowed to observe. The teacher put multiplication questions on the board and allowed the “students” to work them out one by one. The teacher made sure the first equation was an equation that all the “students” could solve easily. This was done because the rest of the multiplication questions were relating to the first one and each other. This way of doing multiplication questions was a way I had never seen before and at first, I was very uncomfortable doing it in the way the teacher was presenting. However, after I saw that the way was more successful than trying to multiply large numbers together, I started to become okay with the process. Once the teacher also showed how the equations relate to each other and work out visually, that made it MUCH more understandable to me. This is very interesting to note because in our classrooms we are going to have a many students who are visual learners and may struggle with the abstract idea of numbers.

Online, we were shown the importance of making mistakes and taking your time while doing math. Research has shown that making mistakes helps your brain grow and develop. As teachers we need to let students know that they should not be embarrassed to make mistakes as they are working through a problem. Making mistakes usually means that the problem is challenging. When the problem is challenging that means it is working their brain and helping it grow. Thus, getting challenged and making and working through mistakes actually makes us more capable of solving math problems. The online module also made it clear that as teachers we need to allow our students more time to complete math problems instead of expecting them to work through them fast. Taking more time on a problem allows for deeper thinking and greater understanding. 

Math Blog Week 1 and Week 2

These last three math classes we have discussed the syllabus, began our unit plans, and discussed the assignments. Once all the housekeeping was done, we discussed the stigma surrounding math and how to change it. I personally believe that so many people dislike math because if you are not fully comprehending one strand or topic then other strands or topics become very challenging. Before moving on in math students should first have a strong understanding of the topic beforehand. Also, through class and the online modules we discussed how no student is “bad” at math, but that some students just need more time to learn math or need to be shown a different way of doing math that makes sense to them. The idea that only some people can be good at math and others will never be good at it is wrong. With enough time, all students can succeed in math. Its just finding the time to learn it. Many students need more time to learn math than others, but school moves on so quickly, that those students do not get a chance to excel and end up falling behind in math. This is where the math divide begins. Another hinderance to teaching the math curriculum is that so many students are frightened or embarrassed to make mistakes when doing math. These students need to be aware that mistakes are what help us learn and help our brain grow and it is our job as teachers to encourage this growth. If all students valued being hard workers over being "smart" I believe there would be more students achieving success in every subject because they would be more willing to challenge themselves instead of scared to embarrass themselves by not fitting the ideals of being “smart.” As teachers, it is our responsibility to teach students to believe in themselves, and to do that, we need to show them that we believe in them too. When they believe in themselves and are shown that working hard is valued and much more important than being “smart,” then the student’s growth mindset will improve, and students will be much more likely to achieve success in anything they put their minds to, especially math. As teachers we also need to encourage our students to have confidence in themselves and their hard work. We want to be in their corner. If we praise and encourage hard work and perseverance, our students can achieve more than they ever thought hey could.