It is hard to believe that almost six weeks have past since I began this course and that in less than two weeks I will be standing in my second classroom, ready to begin teaching a grade 8 class for a seven week period. This unfortunately means that I will be writing my last reflective post, but I am pleased to say that this past week has been the best learning experience that I have had in this course. In the last class my partner and I had the opportunity to deliver a 30 minute presentation, the purpose of which was to facilitate a beneficial learning experience for my peers. The topic that we chose was teaching strategies/math inquiry and by the end of the presentation I think the learning experience was two fold. I wouldn't be surprised if my partner and I learned more from this experience than our peers. We delivered a math inquiry involving place value and the beautiful part about this demonstration was experiencing just how risky inquiry can be. We had hoped that we would have seen a diverse display of strategies being used to solve for the problem but every group decided to figure out the problem in the same way. This meant that we needed to be flexible in our delivery of the lesson and ask questions that guided the students' thinking towards other possible solution strategies. To consolidate we discussed these strategies and then we discussed the other teaching strategies that were being intertwined with the inquiry lesson. Although a struggle to design and facilitate, this learning experience has allowed me to feel just a little more comfortable in my ability to run other inquiry lessons in the future and to be confident in my ability to be a flexible educator who can go with the flow during a lesson. For the purpose of this post I don't want to dive to far into this inquiry lesson and all of the little intricacies that were involved, partly because I have already written a reflection about this experience, but also because there were other great learning experiences for me while participating in the other group members' learning demonstrations.
As I have mentioned earlier in this blog, fractions and I are not the best of friends. Not because I don't understand them, but because I find them difficult to teach. One of the groups presenting in the last class did an excellent job showing how to differentiate the process of learning and did so under the umbrella of teaching fractions. We participated in learning about fractions through three separate learning stations. One stations used paper plates with various visual displays of fractions and required us to group them into separate fraction categories (e.g., 1/4, 5/8 and 2/16). Another station required us to make up a song about fractions after watching three different video examples modelling our task. The last station allowed participants to use an app on the computer requiring us to make different sized pizzas, each with their own separate fraction of toppings. This app was engaging because the faster and more accurate that you could create the correct pizzas, the more money you made. Each group tried their best to outdo the last group and the competition made everyone put in their best effort. Throughout these stations, the one that I had the most amount of difficulty with was the paper plates station. For some reason the various picture representations involving different fractions was hard for me to discern. The more practice I got with them, however, the better I got at picking the correct paper plate. My partner was a big help during this station and I learned from this that it is important to have a collaborative partner during these stations because we learned from each other and the learning experience was far more useful and engaging. In the future when I run a math lesson such as this I will be sure to make collaborative groups where those who fully understand the problem can help those that are struggling and together they can benefit from the partnership.
It was interesting to see the contrast between this kind of partnered learning experience to the more independent kind of learning experienced seen in the demonstrations involving financial literacy. Two group shad this same topic and each group decided to take more of an independent approach. One group used the Kahoot! online app to facilitate a questionnaire and I found this app to be very useful in promoting competition but it was also difficult for me to do well because each question is timed and the faster you answer the question, the more points you get. This element to the learning experience didn't allow me to think through the questions enough to really give an honest account of my learning because I was more worried bout my speed. I learned from this experience that this kind of app is very useful as a minds on or icebreaker activity that excites students and encourages them to be interested in the action or core activity portion of the lesson. The other lesson demonstration involving financial literacy was more of a hands-on demonstration where the group gave each individual five hundred monopoly dollars and were asked to spend our money on a variety of items that we would need for the month. Those items ranged from tuition, to rent, to groceries, to games and so on. The list of items essentially ranged from very useful and based on necessity, to least useful and based on want. During this activity we were also allowed to save any money that we thought appropriate. Along with their icebreaker activity that had us reviewing different terms involved with financial literacy, I was influenced to think more about my needs than my wants and was positively thinking about my future spending habits and my financial goals. I believe that with this kind of positive set-up, younger students who often don't think about these kinds of life skills would also be encouraged to incorporate such spending habits into their daily life. Essentially I learned that giving students these kinds of tools early in life will benefit them in the future and help them to be more mindful individuals who are more concerned with their needs than their wants and can become active participants in future change.
Thursday, October 20, 2016
Friday, October 14, 2016
My Weekly Report and Reflection 5
This past week's math class had me thinking about math differently and reflecting upon my previous learning experiences. We were discussing ways in which future educators can step outside of the box to give students learning opportunities that allow them to use their intuition and formulate ideas by drawing and representing mathematical problems. Too often, educators have their students learn a particular formula for calculating a problem and then give them a worksheet of questions that involve applying said formula. The problem with this, is that when it comes time to give a summative assessment to students, they have had a lot of practice with each individual formula but have had no practice making decisions about which formula to apply. Reflecting upon my own mathematical learning experiences, this form of rote formulaic application defines the way that I learned math. Feeling a little cheated about my elementary/secondary education and thinking about my next upcoming teaching block, I have been thinking greatly about ways that I can take students to the next level in their self guided learning experience. How can I present ideas to my students that allow them to ask their own questions, represent mathematical problems in their own ways, use their intuition and be motivated enough to research those ideas through a student-centered educational journey?
One way that I would like to help myself to step outside of this teaching box is by becoming more familiar with the TPACK educational framework. An acronym that stands for Technological Pedagogical Content Knowledge, TPACK presents itself as a trifecta of knowledge that can help future educators to give new and beneficial learning experiences to their students.
In our course we have learned that the most beneficial forms of learning occur when a student is able to connect new concepts to previous experiences or prior knowledge. Stepping outside of the educator's role for a moment, I feel as though I am a little uncomfortable with this framework because the technological content and concepts being taught to us have no place to connect to my previous education. In class we explored an interesting online resource at geogebra.org and had the chance to play around with creating lines, segments, perpendicular lines, angles, polygons and circles. The one portion of this exploration that resonated most with me was drawing perpendicular lines using two intersecting circles. The question started out by giving us a straight line with two opposing points, one at either end. We were asked if we could draw a perpendicular line by using those two starting points. Instantly, my previous knowledge of using a physical compass to create intersecting circles came back to me and I was able to complete this problem. Reflecting on this experience I think that my previous knowledge came back to me because of the tactile experience of actually using a compass to solve this problem. Part of me wonders if using an online resource such as this one would eliminate one part of learning by removing the physical process of using a compass. Maybe a resource like this one would be beneficial as a form of differentiation after students have had a chance to use a real compass.
With this in mind, I have already begun to look into ways that I can create mathematical investigations by using tech enhanced instruction to help my students guide their own learning experiences. In my upcoming class demonstration, a partner and I have created a mini math inquiry involving place value by using google slides. Giving the entire class an image prompt, we will be exploring and discussing open inquiry and closed inquiry when approaching this problem. While creating this demonstration we reflected on the best ways to set up an open form of inquiry where our colleagues will make statements about what they notice and ask questions about what they are wondering. Due to time restrictions we will then switch into a more closed inquiry where we give everyone a piece of information about the same image prompt. Individuals taking part in this investigation will need to draw the image prompt into their notebooks, use their intuition and formulate ideas about how to solve the question. When solving the question they will need to use mathematical conjectures to convince themselves, convince a friend, and convince an enemy to prove whether or not their solution is correct. Although this mini inquiry is not a tech enhanced as I would like, I feel as though it is our best effort at taking the first steps to create an investigation that will have students guiding their own learning. I look forward to receiving some beneficial feedback from our professor that will help us to improve this investigation for a more tech enhanced learning experience.
One way that I would like to help myself to step outside of this teaching box is by becoming more familiar with the TPACK educational framework. An acronym that stands for Technological Pedagogical Content Knowledge, TPACK presents itself as a trifecta of knowledge that can help future educators to give new and beneficial learning experiences to their students.
 |
| Koehler, M. (2016, July 2). "TPACK Image: Reproduced by permission of the publisher, © 2012 by tpack.org" [Online Image]. Retrieved from http://www.matt-koehler.com/tpack/using-the-tpack-image/ |
In our course we have learned that the most beneficial forms of learning occur when a student is able to connect new concepts to previous experiences or prior knowledge. Stepping outside of the educator's role for a moment, I feel as though I am a little uncomfortable with this framework because the technological content and concepts being taught to us have no place to connect to my previous education. In class we explored an interesting online resource at geogebra.org and had the chance to play around with creating lines, segments, perpendicular lines, angles, polygons and circles. The one portion of this exploration that resonated most with me was drawing perpendicular lines using two intersecting circles. The question started out by giving us a straight line with two opposing points, one at either end. We were asked if we could draw a perpendicular line by using those two starting points. Instantly, my previous knowledge of using a physical compass to create intersecting circles came back to me and I was able to complete this problem. Reflecting on this experience I think that my previous knowledge came back to me because of the tactile experience of actually using a compass to solve this problem. Part of me wonders if using an online resource such as this one would eliminate one part of learning by removing the physical process of using a compass. Maybe a resource like this one would be beneficial as a form of differentiation after students have had a chance to use a real compass.
With this in mind, I have already begun to look into ways that I can create mathematical investigations by using tech enhanced instruction to help my students guide their own learning experiences. In my upcoming class demonstration, a partner and I have created a mini math inquiry involving place value by using google slides. Giving the entire class an image prompt, we will be exploring and discussing open inquiry and closed inquiry when approaching this problem. While creating this demonstration we reflected on the best ways to set up an open form of inquiry where our colleagues will make statements about what they notice and ask questions about what they are wondering. Due to time restrictions we will then switch into a more closed inquiry where we give everyone a piece of information about the same image prompt. Individuals taking part in this investigation will need to draw the image prompt into their notebooks, use their intuition and formulate ideas about how to solve the question. When solving the question they will need to use mathematical conjectures to convince themselves, convince a friend, and convince an enemy to prove whether or not their solution is correct. Although this mini inquiry is not a tech enhanced as I would like, I feel as though it is our best effort at taking the first steps to create an investigation that will have students guiding their own learning. I look forward to receiving some beneficial feedback from our professor that will help us to improve this investigation for a more tech enhanced learning experience.
Monday, October 3, 2016
My Weekly Report and Reflection 4
This week's math class was a beneficial one for me as I learned about interleaving practice and creating rich performance tasks. It is very easy to get caught up in the idea that a math class must be organized into neatly packaged blocks that teach students a concept and then has them performing tasks related to said content. After that information has been ingrained into each student the teacher will give an assessment that relates to that idea. The issue with this approach is that it doesn't leave room for students to make decisions about the strategies they will use to solve the problem. They already know that they will be using a particular set of operations to find the solution. Interleaving practice helps teachers to overcome that stale form of instruction. Interleaving practice involves the instruction of more than one concept at a time and then requires students to decide what kind of strategies need to be used to solve the problem. They will already have all of the tools necessary to address both content areas but will need to take that learning one step further as they ask themselves questions about what is being asked of them and which operations are needed to find a solution. In class I discussed the idea of teaching students the content areas of perimeter and area and having them solve problems that relate to both concepts. Our instructor felt as though this would be an appropriate form of interleaving. As I left the class I continued to think about this issue and was reminded of my past experiences teaching these two concepts to grade 4 students. Perimeter was one that they grasped fairly well, however, area took a lot more finessing to achieve a deeper level of understanding. In this regard I think it is important for educators to perform lots of formative assessments as they teach these two concept areas so that they have enough evidence of learning to determine whether or not their students are ready for an interleaving assessment. Creating rich performance tasks for students in both content areas can give educators the information they need to make that judgment call.
Rich performance tasks are ones that allow students to ask questions, leads to other problems and has many possibilities. Much like the decision making process involved in interleaving practice, rich performance tasks encourage students to ask themselves questions about what the problem is asking them to do. I experienced this in today's class as we were given two mixed fractions: 3 1/4 and 3 31/9. The question asked us to find three other mixed fractions that fit in-between these two given mixed fractions. Right away I was asking myself what needed to be done here and how was I going to determine which three mixed fractions fit in the middle. I immediately turned to decimals so that I could give myself a range. Once I had that I needed to fool around with some other fractions to find if their decimal equivalents fit within my range. It was interesting to see how this kind of question had other possibilities as well. Some students decided to make common denominators to figure out the improper fractions that would fit in-between the original mixed fractions. These improper fractions could then be turned into mixed fractions and I was again reminded about some of the operations that I had forgotten since high school.
Later we expanded on that idea by using various repeating decimals to figure out what fractions would be their equivalents (without using Google's search engine). These problems had me intrigued and I first struggled with figuring them out. After some trial and error I was able to figure out how to get the correct answer and I started to think about what kinds of real-world applications that could be used to create rich performance tasks that have students asking questions about this kind of content area. Fractions have always been a difficult subject area for me as I have mentioned in previous posts and I'm still wondering and interested about ways that I can incorporate these kinds of problems into my classroom to help students work with fraction problem solving.
Rich performance tasks are ones that allow students to ask questions, leads to other problems and has many possibilities. Much like the decision making process involved in interleaving practice, rich performance tasks encourage students to ask themselves questions about what the problem is asking them to do. I experienced this in today's class as we were given two mixed fractions: 3 1/4 and 3 31/9. The question asked us to find three other mixed fractions that fit in-between these two given mixed fractions. Right away I was asking myself what needed to be done here and how was I going to determine which three mixed fractions fit in the middle. I immediately turned to decimals so that I could give myself a range. Once I had that I needed to fool around with some other fractions to find if their decimal equivalents fit within my range. It was interesting to see how this kind of question had other possibilities as well. Some students decided to make common denominators to figure out the improper fractions that would fit in-between the original mixed fractions. These improper fractions could then be turned into mixed fractions and I was again reminded about some of the operations that I had forgotten since high school.
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| (Dekker, 2016) |
Later we expanded on that idea by using various repeating decimals to figure out what fractions would be their equivalents (without using Google's search engine). These problems had me intrigued and I first struggled with figuring them out. After some trial and error I was able to figure out how to get the correct answer and I started to think about what kinds of real-world applications that could be used to create rich performance tasks that have students asking questions about this kind of content area. Fractions have always been a difficult subject area for me as I have mentioned in previous posts and I'm still wondering and interested about ways that I can incorporate these kinds of problems into my classroom to help students work with fraction problem solving.
Monday, September 26, 2016
My Weekly Report & Reflection 3
The days leading up to this week's class, I found myself going ahead in my posts to get a better understanding about what we would be discussing. This week the math mindset module had me exploring the connection between answering math problems quickly and student success in the classroom. When I viewed this video prior to class it made sense to me and I could understand the reasoning behind giving students a chance to ponder over math problems instead of requiring them to give speedy answers to display their ability. I had this in mind when I came to class this past Thursday. The first activity we performed involved mental math operations and required one person to figure out their answer after having a word problem read to the class. They would then reply that they have that number and would read their word problem so that the next individual who had that answer could continue the cycle. Interestingly, there was nothing mentioned about giving quick answers to these problems but you could tell from the very beginning that some of the future teachers in the room wanted to show everyone that they knew the answer first and couldn't stop themselves from blurting out the answer. This continued to happen even after being told not to yell out the answer. I had a little ah-ha moment as the individuals in the room who needed a little extra time to figure it out felt belittled by their peers yelling out their answer before they could figure out that they were holding the next piece to the cycle. I was reminded of the mindset module video and how it is better to give our students a chance to figure out the problem so that they can make deeper connections with the mathematical concepts.
As a future educator, one pedagogical concept found in the growing success resource really struck home for me. In class we had a chance to discuss differentiated content. I kept getting confused that differentiated content was modified curriculum, where teachers give students who are at a lower learning level different work with a different set of big ideas and expectations. Dr. Khan made sure to go over this thoroughly as he could see that there was some interest about this in the class. One point he made was that differentiated instruction involves educators giving their students parallel tasks that "meet the needs of students from different developmental levels but that get at the same big ideas and are close enough in context that they can be discussed simultaneously" (Khan, 2016). At first I even debated with another class mate about this because I felt that this still involved modification but he helped me to see how the overall idea and expectations are still the same with differentiated content. He said that the teacher anticipates the problems that the different learners in the room will encounter and creates other problems that will help those students to see the concept from a different perspective. They are still learning the same information but from a different view. This conversation with the instructor and that student has helped me to put a finger on the kinds of things that I can do to differentiate my content. This can be done by using graphic organizers, varied supplementary materials, compacting the material or flexible groupings for those students that struggle at math. All-in-all I had a lot of great ah-ha moments in this class and I have made the time to write these down in a journal where i can go back and view this information during my teaching block and future career.
Resources Viewed
Khan, S. (2016). EDUC 8P54: Parallel Tasks [PowerPoint Slides]. Retrieved from https://lms.brocku.ca/portal/site/EDBE8P54D12FW2016LEC003/page/39971b0a-3b0e-4242-98b5-ad5cd21dbec1
As a future educator, one pedagogical concept found in the growing success resource really struck home for me. In class we had a chance to discuss differentiated content. I kept getting confused that differentiated content was modified curriculum, where teachers give students who are at a lower learning level different work with a different set of big ideas and expectations. Dr. Khan made sure to go over this thoroughly as he could see that there was some interest about this in the class. One point he made was that differentiated instruction involves educators giving their students parallel tasks that "meet the needs of students from different developmental levels but that get at the same big ideas and are close enough in context that they can be discussed simultaneously" (Khan, 2016). At first I even debated with another class mate about this because I felt that this still involved modification but he helped me to see how the overall idea and expectations are still the same with differentiated content. He said that the teacher anticipates the problems that the different learners in the room will encounter and creates other problems that will help those students to see the concept from a different perspective. They are still learning the same information but from a different view. This conversation with the instructor and that student has helped me to put a finger on the kinds of things that I can do to differentiate my content. This can be done by using graphic organizers, varied supplementary materials, compacting the material or flexible groupings for those students that struggle at math. All-in-all I had a lot of great ah-ha moments in this class and I have made the time to write these down in a journal where i can go back and view this information during my teaching block and future career.
Resources Viewed
Khan, S. (2016). EDUC 8P54: Parallel Tasks [PowerPoint Slides]. Retrieved from https://lms.brocku.ca/portal/site/EDBE8P54D12FW2016LEC003/page/39971b0a-3b0e-4242-98b5-ad5cd21dbec1
Friday, September 16, 2016
My weekly report and reflection 2
In this week's math class I found myself doing three important things that really struck home with me. I revisited an old concept that frustrates me and I was performing some creative in class activities. To begin this post I will address the concept that frustrates me the most in mathematics. That concept is fractions. In our last meeting we were discussing the ways of approaching this topic with students and how to help them discern the difference between 5/8 and 6/10. The question was asking students to decide which fraction is bigger. I know it's 5/8, I can completely understand why it's 5/8 but trying to explain this concept in an intelligent and concise way to students is a struggle for me. I even did my best to stand in front of the class and explain how in the fraction 5/8 you have 8 whole parts (I used a pie) with 5 of them coloured in, leaving you with only 3 pieces lefts over. On the other hand, with the fraction 6/10 you have 10 whole pie pieces with 6 of them coloured in, leaving you with 4 pieces left over. Thus, the first fraction (5/8) is bigger because you had less parts left over. Well, by the time I was finished speaking I probably used about 50-75 words too many and had the ugliest looking set of scribbled pies on the board. I learned from that experience that less is more and that I needed to redefine the way that I think about fractions and refine my explanation. Our instructor then showed us the same two fractions represented by squares. For the fraction of 5/8 there were 8 squares with 5 coloured in and for 6/10 there were 10 squares with 6 coloured in. The difference between his diagrams and mine was that both diagrams took up the same amount of overall space, however, the pieces drawn in the fraction 6/10 were smaller. This was because there were more parts that needed to be placed in the same amount of space as 5/8. Visually, it was easy to tell from the very beginning that 6/10 was smaller because the pieces were smaller. He then reminded me of another way to demonstrate the difference between two fractions. Translate them into decimals and use a number line. Personally, I like this way better because it makes more sense to me. Just divide 5 by 8 and 6 by 10 and you get 0.625 and 0.6 respectively. Place those two numbers on a number line and show how 0.625 is closer to 1 than 0.6. In the future I will probably do it this way because it related better to the way that I process information but I won't dismiss the idea of showing the square diagrams because every student thinks differently and what works for me might not work for every student.
During our in class activities we were asked to look at three separate rotational views of the same picture containing owls on a 4x4 square platform. The question asked us to figure out how many owls were standing on the platform. We were given connecting cubes as manipulatives to help visual/kinetic learners to solve the problem more easily. I chose to not use the connecting cubes but to watch what others were doing and to discuss the problem with one of my classmates. Through community-based learning I was able to better understand the problem and got the correct answer. Just having that one student mention to me which way the one picture was rotating helped me to understand the question much quicker and easier than having to build the entire 4x4 platform. By reading the curriculum document I discovered that this problem relates to the grade 6 specific expectation of "build[ing] three-dimensional models using connecting cubes, given isometric sketches or different views of the structure" within the geometry and spatial sense strand (Ontario Ministry of Education, pg. 92).
The second in class activity that I really liked and that I will definitely incorporate into one of my classes in the future was a finger counting activity. The task was to count on our fingers from 1 to 1000, starting at the thumb with 1. The catch (and there's always a catch) was that once we reached the pinky finger at 5 we needed to then count in the opposite direction on our hand with the ring finger being 6 and the thumb consequently becoming 9. We then continued counting on our fingers in the same direction that we first started making the pinky 13 once we had returned again. The question asked us what finger we would land on once we reached 1000. What I really liked about this task was seeing the different strategies that people were using to get their answer.
As you can see here in this picture, the diagram on the right shows the group trying to use division to reach a solution and the group on the left was trying to decide which numbers would fall on each finger. Our group started to count each finger to establish which fingers were showing a common pattern.
We discovered that the index finger and the ring finger had a pattern involving groups of ten. At first we thought that those groups of ten were going back and forth from the index finger to the ring finger and back again (i.e., 10 on the index, 20 on the ring, 30 on the index, 40 on the ring). Later we found out that the pattern was a little different were 10 was on the index finger, 20 was on the ring finger and then 30 would also be on the ring finger before placing 40 on the index finger. We finally came to the conclusion that 1000 landed on the index finger and other groups came to the same conclusion after some time and by using various strategies. It would be interesting to see how younger people would try to figure out this problem and would provide some really rich conversations about mathematical strategies and the way that each individual is different and will approach problems in different ways. All in all, this last math class was a really good learning experience and I felt as though I walked away with some good teaching strategies and felt a little more confident in my ability to teach fractions in the future.
Resource Viewed
Ontario Ministry of Education. (2005). The Ontario curriculum grades 1‐8: Mathematics [Program of Studies]. Retrieved September 16, 2016, from http://www.edu.gov.on.ca/eng/curriculum/elementary/math18curr.pdf.
During our in class activities we were asked to look at three separate rotational views of the same picture containing owls on a 4x4 square platform. The question asked us to figure out how many owls were standing on the platform. We were given connecting cubes as manipulatives to help visual/kinetic learners to solve the problem more easily. I chose to not use the connecting cubes but to watch what others were doing and to discuss the problem with one of my classmates. Through community-based learning I was able to better understand the problem and got the correct answer. Just having that one student mention to me which way the one picture was rotating helped me to understand the question much quicker and easier than having to build the entire 4x4 platform. By reading the curriculum document I discovered that this problem relates to the grade 6 specific expectation of "build[ing] three-dimensional models using connecting cubes, given isometric sketches or different views of the structure" within the geometry and spatial sense strand (Ontario Ministry of Education, pg. 92).
The second in class activity that I really liked and that I will definitely incorporate into one of my classes in the future was a finger counting activity. The task was to count on our fingers from 1 to 1000, starting at the thumb with 1. The catch (and there's always a catch) was that once we reached the pinky finger at 5 we needed to then count in the opposite direction on our hand with the ring finger being 6 and the thumb consequently becoming 9. We then continued counting on our fingers in the same direction that we first started making the pinky 13 once we had returned again. The question asked us what finger we would land on once we reached 1000. What I really liked about this task was seeing the different strategies that people were using to get their answer.
 | |||
| (Dekker, 2016) |
As you can see here in this picture, the diagram on the right shows the group trying to use division to reach a solution and the group on the left was trying to decide which numbers would fall on each finger. Our group started to count each finger to establish which fingers were showing a common pattern.
 |
| (Dekker, 2016) |
We discovered that the index finger and the ring finger had a pattern involving groups of ten. At first we thought that those groups of ten were going back and forth from the index finger to the ring finger and back again (i.e., 10 on the index, 20 on the ring, 30 on the index, 40 on the ring). Later we found out that the pattern was a little different were 10 was on the index finger, 20 was on the ring finger and then 30 would also be on the ring finger before placing 40 on the index finger. We finally came to the conclusion that 1000 landed on the index finger and other groups came to the same conclusion after some time and by using various strategies. It would be interesting to see how younger people would try to figure out this problem and would provide some really rich conversations about mathematical strategies and the way that each individual is different and will approach problems in different ways. All in all, this last math class was a really good learning experience and I felt as though I walked away with some good teaching strategies and felt a little more confident in my ability to teach fractions in the future.
Resource Viewed
Ontario Ministry of Education. (2005). The Ontario curriculum grades 1‐8: Mathematics [Program of Studies]. Retrieved September 16, 2016, from http://www.edu.gov.on.ca/eng/curriculum/elementary/math18curr.pdf.
Tuesday, September 13, 2016
My weekly report & reflection 1
Hello everyone, I'd like to welcome and thank you all for taking the time to read this first blog post about the pre-service mathematics course in year 2 of the consecutive education program at Brock University. Sadly, the purpose of this post and those to follow will not be to grind and inundate you with a plethora of new mathematical concepts or to even help you finally solve those pesky Diophantine equations. I know, now that you've heard the bad news please take a moment to compose yourself before you continue reading. In all seriousness, the purpose of these posts will be about helping myself and hopefully the reader to successfully find the power in the art of self-reflection. The process of self-reflection is an important one. It allows not only pre-service educators but educators in all stages of their career to improve their teaching practice and to reflect on the strategies they use to foster wonderment and discovery in their students. In our first class, 'wonder' and 'discovery' were two buzz words that came up repeatedly.
The first in class activity that really had me exploring these two ideas (more so wondering than discovering) was a sorting activity that had our table groups looking through a series of printed squares containing the math curriculum expectations of grades one to eight in a single strand. Our strand was geometry and spatial sense. From the very beginning I was honestly overwhelmed by the amount of information that we had to discern. Doctor Khan made sure to give us just enough information in that particular moment to leave us wondering about what we were doing with our lives. He told us to sort these squares in which ever way we saw fit. Well this just went against everything that I had ever been taught in math. There is only one way to solve any math problem and I did not have the key to solving this equation. I was left wondering whether or not the information needed to be sorted by the similar words in bold or by the content that each presented. I expressed my displeasure to Doctor Khan and he simply said "well good, write down what you are wondering". At that moment I kind of went "oh, that's the whole purpose of this, I'm suppose to wonder and struggle with the problem". Our group's final product looked very ordered and chronological.
After sorting our information we had a chance to do a gallery walk of the other group's work and I still had difficulty seeing the solution to my problem. We discussed what each group did and by reflecting I noticed that some of the content we placed at the end in grade eight could have gone before grade two. Such information like demonstrating the applications of geometric properties in the real world as described in GSS 022. In grade two students need to sort and classify quadrilaterals based on the geometric properties. At the very least an educator could have their students sort and classify real world geometric shapes. Throughout my investigation of our group's final product I found many other instances where the orders could have been changed based on the curriculum's suggested tools of engagement. I then realized that educational practitioners need to know the space that they are working in and to look across the curriculum to use sensibilities found in later grades to help encourage students in earlier grades. The guidelines given are not as cut and dry as I once thought.
During the week that followed we needed to watch a series of videos discussing the commonly propagated attitudes towards math that unfortunately create stereotypes and form math myths. You might be 'wondering' what this is all about so let me shed some light on the situation. In today's classrooms some of the common attitudes towards math are that it's only for those who are math people, that it's a difficult subject because a question can only be answered one way, and that because of these reasons it has no useful application in the majority of people's lives. To make things worse the media commonly propagates these attitudes throughout all forms of entertainment. It has become such a problem that one of the common stereotypes to arise from all of this is that boys are good at math and girls are not. This stereotype is one that I heard while growing up but was difficult for me to believe in (despite being helped by my Grandfather in the subject while my Grandmother helped with English). Many of the female students in my elementary and secondary classes have actually been quite good at math and on quite a few occasions have surpassed my ability completely.
One math myth that I did believe in while growing up was that people are either left brained or right brained and that people who fell into one category or the other had difficulty performing tasks associated with the opposite side. I was actually reminded about this myth by a fellow classmate of mine while responding to one of their forum posts. As a musician I believed that I fell into the right sided category that relates to creativity and artistic sense. I believed that being in this category meant that I could never be a mathematician or form a career involving mathematics because that belonged to the left brained people. By watching the required videos this week I learned that every individual can have a math brain.
Much like any muscle in the body, the brain can grow and be strengthened by repetitive problem solving. The key is that educators create lessons that fuel student interest and inquiry. Students need to have the opportunity to 'wonder' about an equation and then take the time to struggle with that problem so that they can 'discover' the solution on their own. Just like the sorting activity that I first struggled with and later understood its purpose. I learned that it's good for students to sometimes feel uncomfortable while inquiring about a problem and then experience the sense of relief and accomplishment that follows when discovering the solution. In doing so it helps strengthen the brain by forming new synapses to aid in the transfer of information through an electrical impulse between neurons. Hopefully during my teaching block I can encourage my students to have all of their synapses firing through lesson that promote 'wonder' and cultivate 'discovery'. At the end of the day I just hope that I'm able to see through all of the smoke that those synapses create.
The first in class activity that really had me exploring these two ideas (more so wondering than discovering) was a sorting activity that had our table groups looking through a series of printed squares containing the math curriculum expectations of grades one to eight in a single strand. Our strand was geometry and spatial sense. From the very beginning I was honestly overwhelmed by the amount of information that we had to discern. Doctor Khan made sure to give us just enough information in that particular moment to leave us wondering about what we were doing with our lives. He told us to sort these squares in which ever way we saw fit. Well this just went against everything that I had ever been taught in math. There is only one way to solve any math problem and I did not have the key to solving this equation. I was left wondering whether or not the information needed to be sorted by the similar words in bold or by the content that each presented. I expressed my displeasure to Doctor Khan and he simply said "well good, write down what you are wondering". At that moment I kind of went "oh, that's the whole purpose of this, I'm suppose to wonder and struggle with the problem". Our group's final product looked very ordered and chronological.
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| (Dekker, 2016) |
During the week that followed we needed to watch a series of videos discussing the commonly propagated attitudes towards math that unfortunately create stereotypes and form math myths. You might be 'wondering' what this is all about so let me shed some light on the situation. In today's classrooms some of the common attitudes towards math are that it's only for those who are math people, that it's a difficult subject because a question can only be answered one way, and that because of these reasons it has no useful application in the majority of people's lives. To make things worse the media commonly propagates these attitudes throughout all forms of entertainment. It has become such a problem that one of the common stereotypes to arise from all of this is that boys are good at math and girls are not. This stereotype is one that I heard while growing up but was difficult for me to believe in (despite being helped by my Grandfather in the subject while my Grandmother helped with English). Many of the female students in my elementary and secondary classes have actually been quite good at math and on quite a few occasions have surpassed my ability completely.
One math myth that I did believe in while growing up was that people are either left brained or right brained and that people who fell into one category or the other had difficulty performing tasks associated with the opposite side. I was actually reminded about this myth by a fellow classmate of mine while responding to one of their forum posts. As a musician I believed that I fell into the right sided category that relates to creativity and artistic sense. I believed that being in this category meant that I could never be a mathematician or form a career involving mathematics because that belonged to the left brained people. By watching the required videos this week I learned that every individual can have a math brain.
Much like any muscle in the body, the brain can grow and be strengthened by repetitive problem solving. The key is that educators create lessons that fuel student interest and inquiry. Students need to have the opportunity to 'wonder' about an equation and then take the time to struggle with that problem so that they can 'discover' the solution on their own. Just like the sorting activity that I first struggled with and later understood its purpose. I learned that it's good for students to sometimes feel uncomfortable while inquiring about a problem and then experience the sense of relief and accomplishment that follows when discovering the solution. In doing so it helps strengthen the brain by forming new synapses to aid in the transfer of information through an electrical impulse between neurons. Hopefully during my teaching block I can encourage my students to have all of their synapses firing through lesson that promote 'wonder' and cultivate 'discovery'. At the end of the day I just hope that I'm able to see through all of the smoke that those synapses create.
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