When I first started this class (and the BEd in general) I was so nervous! I remember feeling so ill-prepared to become a math teacher and I was worried I made the wrong decision. From this class, I gained confidence and comfort in my skills, specifically through the group and individual micro-teaching. The biggest thing I learned this semester is that math isn't black and white, it can incorporate outdoor education, art, and even movement. My favourite articles to read this semester were the Skemp article, Flow ted talk, and Battleground schools. All three of these articles made me reconsider what mathematics education truly is, and I hope to incorporate these new concepts into my own classroom.
Saturday, December 23, 2023
Friday, December 22, 2023
Textbooks
As a teacher, I understand why the examples are focused on who the textbook is aimed for, and specifically the language used in textbooks. A wordy textbook may be one that turns students away and is not accessible to students, especially students who are ELL. I also think the language of textbooks can either be engaging or disengaging for students. For example, if the textbook is full of problems that students cannot relate to, like the train is travelling east at 30 km/h example, students can become quite disengaged. Additionally, teachers should be previewing the textbooks given to students because let's say a textbook was written in Montreal and focuses on examples around Montreal, this can be disengaging for students that live in Metro Vancouver.
As a student, I always used my textbook as a tool to study with. I remember from a young age my mom and I sitting with a math textbook and working through the problems so I could be prepared for tests. I always saw the textbook as a holy grail, holder of all knowledge, until I got to calculus in grade 12. In grade 12 I really disliked the textbook we were using in class and I supplemented what we were using in class with resources online. Additionally, as a student, I always found textbooks to be too wordy. I also always found myself losing steam by the time I got to the challenge questions and would often leave them, not necessarily because I did not understand them. I think as a student I would have benefitted from harder and easier questions being dispersed throughout the textbook.
I think textbooks are a great tool for students to have something to fall back on. Textbooks are also great for parents who want to be involved in their child's learning and see what we are doing in the classroom. However, with our everchanging curriculum, textbooks must be supplemented with additional resources. Teacher made resources can often be tailored to student needs, and can provide students with more direct instruction than a textbook can.
David Hewitt and Mathematical Awareness
One stop I had while watching the video is the idea of powers of the mind. Hewitt brings up a good point that students are often relying solely on memory in the classroom rather than thinking and working out why math works the way it does. I think a lot of this comes from the traditional teaching technique of stand and deliver, students are able to take the backseat while the teacher is doing all the thinking and hard work. Using thinking classrooms can help put students in the driver's seat and take control of their learning.
I also enjoyed that Hewitt did not explicitly tell students if they got the question correct but instead lets them figure it out on their own. I think this is important in the classroom because it moves away from the idea that the teacher is the holder of knowledge and rather encourages students to be independent.
Finally, I also liked the idea of doing math verbally. I can see that working very well for certain students who are auditory learners. It can also work well for students who get overwhelmed by mathematics when it has been written down. However, I can also see how for certain students this method of learning can be inefficient because they get confused when things are not written down.
In my own classroom I would love to try out thinking classrooms and fostering independence in students. I feel these methods are quite beneficial for students because it helps them take accountability for their learning.
To solve the fraction problem of finding a number between 5/7 and 3/4 my first step was to make sure they both had the same common denominator. So the numbers would now be 20/28 and 21/28. Hence a number between 5/7 and 3/4 could be 41/56.
I think Hewitt created these problems to be solved as a problem of day or as a way to start off an inquiry-based lesson. All the problems in the video are great examples of problems that have multiple correct answers which can help students understand that there are multiple ways to approach even one problem!
Monday, December 18, 2023
Friday, November 24, 2023
Flow
I have felt flow in my math classes when I am particularly engaged or interested in a topic we are learning. I also feel flow during crocheting, singing, going on walks, and while exercising. I think being in flow depends on how interesting a topic is, or how it is presented to students. If a student is not interested they can never achieve flow.
I think we can help students achieve flow by teaching math in engaging ways so students have an interest in the topic and are challenged by the content that is being taught to them. Teaching math through inquiry or project based learning can help students be more engaged and can help them reach a state of flow. I feel that achieving flow in math class is possible for all students, but we will need to cater to each students needs individually so they can meet flow in their own way.
Tuesday, November 21, 2023
Arbitrary vs Necessary
Hewitt refers to arbitrary as something that is taught to be memorized, something that must be done exactly the way it is taught. For example, using the + sign for addition and the - sign for subtraction is purely convention, and students are required to memorize these signs to progress further in mathematics. Necessary is referred to as content where the students do not necessarily need to be informed. For example, students can learn how to add fractions with or without mixed numbers without the convention of writing it down. Necessary knowledge can come from within or be discovered through inquiry. Arbitrary must be taught to all students, necessary can become aware to certain students through other concepts.
The concept of arbitrary vs necessary is new to me in theory, whoever, I feel that inherently I was always known about it in theory. Using a student led approach or inquiry based approach in the classroom can help students learn the necessary and can help all students understand the arbitrary.
In my own classroom, I could create questions that teach all the students the arbitrary but leave room for certain students to learn the necessary. We want to move beyond teaching and having students regurgitate that information on tests without having any understanding of why the concept works.
A personal example of this for me was in grade 12 when we learned the unit circle. I remember my teacher emphasizing that we must memorize the unit circle and even having quizzes where we would have to fill in the unit circle in 5 minutes. I purely did that, I sat down and I repeatedly practiced writing the unit circle until I knew with certainty that I could replicate it on the test. I had no idea how the values of the unit circle were derived or even what they meant, I just had them memorized. If this was my own classroom, I would have focused on the meaning behind the unit circle and I would have had students find connections between how different trig values create the unit circle.
Giant Soup Can of Hornby Island
I have put a picture of my calculations and following that there is a description of my rationale.
I started this problem by considering the average size of a women's bike, after some research I realized that the height of an average bike is hard to find on the internet, and usually you can only find the length of the frame. The frame of a bike for a woman between 5'3 and 5'5 would be 71 cm (Hudson, 2022), from there I guessed that the total height could be 100 cm.
From the picture, the diameter of the tank looked to be about 3 times the height of the bike, so I estimated that the diameter of the tank to be 300 cm. From some more research, I found that the average bike length is 175 cm (Ellis, 2022). In the picture, the height (or length as written in my work) of the tank looks to be about twice the length of the bicycle, so I estimated the length of the tank to be 350 cm.
At this point, I wanted to make sure my calculations were comparable to that of a regular soup can, so I took ratios of both the tank and can (height to diameter) and compared them. They were very similar, only about .3 of a decimal difference!
My next step was to calculate the volume of the tank which ended up being 24.74 m^3. Now I wanted to see if this would be enough to put out a house fire. Through some research, I found out that you need 400 gallons per minute of water to fight a house fire (Smith, 2010). I then converted my volume into gallons to find out that the tank can fight a house fire for about 15 minutes. Once again, based off of some research, I found out that it takes about 20-40 minutes to fight a house fire (Chase, n.d.). So, if there was a small fire, the tank would have enough water to fight it.
My student bird struggled with this problem because this was really new territory for me, while I understand all the mathematics behind the problem, I have never applied it in this manner and it was a new experience for me.
However, my teacher bird enjoyed this problem because it made me think critically, problem solve, and apply my skills outside of the box. I think this would be an excellent puzzle for students who need an academic challenge or as a problem of the week where the class would discuss and solve it together.
Extension:
Here is a sculpture in downtown Calgary, a head you can stand inside of! A problem I would pose to my students could be, given my height 5'1 and the average size of a human skull, what are the dimensions of the sculpture? I would give the students a picture where I am standing inside the sculpture (I just don't have one at this moment!) so they could reference off my height.
References:
Chase. (n.d.). How Long Does It Take To Put Out a House Fire? https://firefighterinsider.com/how-long-put-out-house-fire/
Ellis, C. (2022, August 20). What size shed do I need for my bikes? | The Best Bike Lock. The Best Bike Lock. https://thebestbikelock.com/bike-storage-ideas/best-bike-storage-shed/what-size-shed-for-bikes/
Hudson, A. N. (2022). Rutland Cycling. Rutland Cycling. https://www.rutlandcycling.com/pages/sizing-guide/
P. Smith, J. (2010, December 1). Needed Fire Flow. Firehouse. https://www.firehouse.com/home/article/10465153/determining-how-much-water-is-needed-for-effective-fire-control
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