Weeks 10-11 Reflection

Week 10 was a week I had been looking forward to from the first day of class. We began with the learning activity as usual, but this week was my turn to develop and lead it. Week 10 dealt with probability, which is why I chose it for my activity. Probability is something I have always found interesting and applicable to real life. It is cool, because it is something you can think and theorize about and then simply test and see the results almost instantly. My activity involved a minds-on component which drew on knowledge from the prior grade level (grade 4), while also being open-ended and allowing for many different solutions and answers. The action component focused on expanding into the grade 5 curriculum, while building slowly and sequentially to not introduce and new concepts too quickly.

- My action worksheets.

After my activity, we moved onto the lesson and talked about some of the big ideas for this topic. The lesson focused on, collection and organization of data, data relationships and probability. After some brief review and discussion, we moved through a couple of activities to apply the concepts and practice the use of manipulative's in probability. Following the activities, we reviewed the concepts of mean, median and mode and how they relate to interpreting data and probability. Finishing the lesson, we looked at some games and literature that we could draw on to gain ideas of how to teach and differentiate within the classroom.

Moving to week 11, it was really interesting. We did the makerspace program and got to go into a very open ended session where our creativity and math knowledge were tested. The point of makerspace is to show how useful and beneficial tools and technology can be when try to teach and differentiate math curriculum. The first station that my group and I went to was the 'construction station'. We had popsicle sticks and glue guns and had to think how to relate it to the Ontatrio math curriculum. We came up with the idea of area and perimeter (geometry and measurement) and how you'd need to take that into account when getting the appropriate number of tools to create what you envision. The second station we went to was a ozobots station where we had to draw lines that our little robots could follow. We said that students could relate this probability if you had the robots race or choose a line to follow when multiple were presented. Lastly, we went to the 3-D printer station and were able to make whatever we could imagine. This one was very open ended and could have been related to a number of concepts such as geometry, measurement, angles and much more.


The picture above, provides a link to the makerspace website.

Finishing the lesson, the slide show went over assessment in mathematics, going over topics such as; comprehensive assessment, assessment as/of/for learning, alternative assessment, rubrics and checklists (checkbrics), journal writing for anecdotal evidence, and how to make an appropriate reflection. All of these were very useful concepts as they relate to what we've been learning in our assessment class, but are more tailored towards math specifically.

Weeks 8-9 Reflection

In week 8 we talked about Geometry and spatial sense. We had a great learning activity as we discussed the properties and rules regarding finding area and perimeter. We had a minds on with simple polygons and then moved to finding the perimeter of a house, as well as all of the rooms inside of it. At the beginning of the actual lesson however, we reviewed some of the big ideas in the JI strands; Properties of two-dimensional shapes and three-dimensional figures, geometric relationships, location and movement, application of geometric properties in real life. Additionally, we reviewed the 5 levels of Van Hiele's theory, being; Level 0 (recognition), Level 1 (Analysis), Level 2 (Relationships), Level 3 (Deduction), Level 4 (Aximatics). Adding onto these concepts, we then reviewed some terms like; transformations, congruency, similarity, symmetry, as well as different shapes (rectangle, square, diamond, parallelogram, regular pentagon, and trapezoid.
After this, we moved onto 'learning through examples' and tried to figure how many different kinds of triangles we could make with a specific set of lines.

In week 9 we looked at measurement and started out with our learning activity again. In our class presentation, we started with a definition of measurement; "Measurement is the assignment of a number to a characteristic of an object or event, which can be  compared with other objects or events". After that we had a discussion about what might me missing from this definition, as well as the stages in the development of measurement. We first talked about comparison (direct, seriation, indirect), Non-standard (quantification, constant unit), and standard SI-units. From this point, it was a good way to transition into the benefits and importance behind using the metric system. The metric system is simple to use as there is only one type of measurement for each type of quantity, and there are only a few base units. After these clarifications, we moved onto teaching through problem solving; here we talked about estimation in regards to measuring the length of the rooms. This gave us a good look into the importance of having an idea of the relative size of objects and the space around you. From here we moved into the concept of visualization as well as experience. All of these aspects are very important when trying to estimate area and perimeter because they all build onto each other and will make understanding the concepts more palatable.

In conclusion, the two weeks were very good as they built on each other nicely. We also had our focus shift outside of class, as we were tasked with selecting two games from our games forums to review and make a presentation about. This was interesting as it allowed us to recall past units and concepts as well as obtaining a perspective about the games from each group member. As a group, we decided on space race multiplication as well as dirt bike proportions. These two games were both very pleasing aesthetically as well as very easy to play, and extremely relevant to the course curriculum. Another large factor for these games, came down to the ability to either play them single player or with friends. We feel like this is important, because similar to our 'learning through examples', as we bounce our ideas off group members and have conversations, it creates more engagement in the content.

Weeks 6-7 reflection

Weeks 6 and 7 were a little tougher than the previous 2 weeks. the content was great and was explained very well, but it is always tough to come back from reading week! I have to say however, that it is bothering me how some of my classmates seem to be losing patience recently and get overwhelmed without trying the content. There were a couple cases in class during the past couple of weeks where students were not initially understanding ratios and proportions and let their emotions get the better of them. They would almost come into the lesson with a closed mindset and began taking it out on the instructor. I just wanted to start off this reflection with stating that the instruction has been very good, the content has not been too difficult and I think some people need to take a step back and try to understand and hear concepts out, before freaking out over the difficulty.

Week 6 was a very interesting week! We started out, as always with our group learning activity, which was very engaging. Our leader for the week, Mike, was very thoughtful and engaging in his activity. He had us looking at ratios and proportions and made it relevant to the Halloween through Harry Potter and potions. Mike started out the activity by explaining the overall and specific expectations for grade 4, as well as giving us a base potion. He said the potion fed 3 people and asked us to figure out the ingredients needed to feed 1 person and then 9 people. We then went into the lesson and talked about the overall expectations more in depth. Them being;
- Demonstrate an understanding of proportional reasoning by investigating whole number unit rates. (grade 4)
- Demonstrate an understanding of proportional reasoning by investigating whole number rates. (grade 5)
- Demonstrate an understanding of relationships involving percent ratio and unit rate. (grade 6)
- Demonstrate an understanding of proportional relationships using percent ratio and rate. (grade 7)
- Solve problems by using proportional reasoning in a variety of meaningful contexts. (grade 8)
After this, we spent the rest of class doing many different examples with our groups and then shared the answers and strategies with the class.

retrieved from: https://www.teacherspayteachers.com/Product/Silent-Teacher-Poster-Ratios-and-Proportions-2017093

Week 7 was a fun week and started off with an amazing group learning activity. This week we learned about patterning and algebra. The activity included a minds on component of looking at number patterns and then moving into the core activity of patterning with shapes and colours. After the activity we went over strategies to help students problem solve when trying to figure out patterns. We talked about concepts like investigation and extending and how/when to apply these concepts. Moving forward we talked about the Ontario curriculum expectations for patterning and algebra;
- Describe, extend and create a variety of numeric and geometric patterns, make predictions related to patterns and investigate repeating patterns involving reflections. (grade 4)
- Relationship in growing and shrinking patterns involving translations. Understand use of variables in expressions. (grade 5)
- Use variables in simple algebraic expressions and equations to describe relationships. (grade 6)
- Represent linear growing patterns using concrete materials, graphs and algebraic expressions. (grade 7)
- Represent linear growing patterns using concrete graphs, algebraic expressions and equations. (grade 8)
Once again, we then spent the remainder of class, building on these concepts and using manipulative's to express our understanding (my favourite part, as I always learn a new way to teach and explain myself).


Retrieved from: https://www.youtube.com/watch?v=No4VLQLrdr0

Weeks 4-5 Reflection

Weeks 4 and 5 were very interesting weeks as I began to get a good feel for the course and the structure. I really enjoy how we began each class with the small group activity as it gives us a good chance to get engaged, get our minds on and even catchup with classmates about our weekends. The course seems to be flying, but as mentioned in my last post, has not become as overwhelming as  some were initially thinking it would be. Theses weeks are set up to be very engaging, educational and incremental in knowledge. I am fairly lucky however as I have a science (kinesiology) background, meaning I did math all throughout my undergrad and have a great base, so this has all been mainly review for me.

Beginning with week 4, we looked at fractions. In our small group activity, we had a worksheet that looked at addition, subtraction, multiplication and division of a variety of fractions (mixed, improper and regular). This was a great mind ons activity as it got me warmed up and ready to tackle the lesson. Within the lesson we covered some of the following 'big ideas':

1. Fractions can represent parts of regions, parts of sets, parts of measures, division, or ratios
2. A fraction is not meaningful without knowing what the whole is
3. Renaming fractions is often the key to comparing them or computing with them. Every fraction can be renamed in an infinite number of ways
4. There are multiple models and/or procedures for comparing and  computing with fractions, just as with whole numbers
5. Operations with fractions have the same meanings as operations  with whole numbers, even though the algorithms differ.

After that, we learned how to identify and meet the specific and overall expectations for the J/I age groups. We accomplished this through problem solving, gamification and children's literature. Additionally, we got into small groups throughout the lesson for some consolidation and solidification of the content we learned. This was very helpful as we had a low pressure opportunity to make sure we understood what we had just learned, as well as collaborate and compare our ideas.

Moving on to week 5, we looked at integers, also falling under the number sense and numeration curriculum. Again, we began with our small group activity, which was one of the most engaging and fun ones I've done. We had a number line on a mountain, a spinner for negative or positive and a dice for our number of moves. We played in 1vs1 teams and had to try to be the first to reach the peak of the mountain. This was also a great minds on activity as it was very visual, very engaging and even competitive. In the actual lesson, we talked about what integers are (whole numbers, no decimals and can be either negative or positive). The big ideas we looked at in this lesson were that:

1. The negative integers are 'opposite' of the whole numbers
2. The zero property is (-1) + (+1) = 0
3. The meanings for the operations (=, -, +, /) also applies to all integers.

We learned many ways to meet the overall and specific expectations for the J/I grades once again, and the applied these concepts in our small groups. Specifically talking about addition, subtraction, multiplication and division of integers, this was again mostly a review. However, I especially liked using the red and blue circle manipulative's as I have never used this method before and definitely learned something.

Below, retrieved from https://www.math-drills.com/fractions/fractions_multdiv_001.php is an example of the fractions worksheet from the small group activity.
 

Below, retrieved from https://www.pinterest.ca/pin/13792342583309192/?lp=true is an example of the number line used in the small group activity.

Weeks 2-3 Reflection

So far this math course has been easier to digest than I think some were initially assuming. There was a definite sense of uneasiness and stress when the topic of math was brought up in the first weeks of school. The topics discussed have been broken down very well and are not overwhelming as they incorporate a great deal of collaboration. 

In session 1 we just took a look at the syllabus and what was ahead in this course, so we will move on and discuss sessions 2 and 3. The second session was a great introduction to see the different types of strands of mathematics (number sense and numeration, measurement, Geometry and spatial sense, Patterning and algebra and data management and probability) as well as steps to problem solve effectively (problem solving, reasoning and proving, reflecting, selecting tools and computational strategies, connecting, representing and communicating). We then used these tools and learned the skeleton for the basis of a basic 3 part lesson plan and problem solving; minds on, action and consolidation and connection. From there we talked about some examples of activities we could implement into a classroom such as a gallery walk, math congress or a bansho. All this information was extremely valuable as it gave a variety of ways to teach a variety of different learners. This lesson was amazing at setting up the expectations of us and the student (in the curriculum expectations document we looked over) as well as how to implement and fulfil those expectations. For those tactile learners in the class, we actually ran through some example problems and used some of these methods to see how they’re effective first hand. 

In session 3 we looked more specifically into the strand of number sense and numeration. Beginning first with the concept of operational sense, we learned about the commutative property, the associative property and then were introduced to some manipulatives to get a visual/tactile look at them. We then went over some concepts to break down more complex problems like partial sum addition, column addition, trade first subtraction, counting up subtraction, partial differences subtraction, partial product multiplication, lattice multiplication, area model multiplication, partial quotient division, traditional method division, area model and column method division. Like mentioned from the last session, the large variety of options with how to tackle problem was amazing as it recognizes the differences between students thinking and encourages many different approaches. Again at the end of the lesson, we broke into groups and had to implement some of these tools which was very useful. This allowed see from a student's perspective and hopefully will better prepare us to guide them more effectively through similar problems. 

In the first two sessions (2-3) I have definitely learned a lot about math, but even more about how to approach a multitude of problems. I definitely have taken away the fact that math is very collaborative and very applicable to logic reasoning and reflection when tackling any issue across many disciplines. I look forward to learning more and sharing my experiences with you!

- Jacob Kerr 

Welcome

Welcome to my math blog! I loved math growing up and always found it similar to a puzzle, trying to figure out the missing pieces (numbers). As I got older I still enjoyed math, but found there were some learning techniques that did not mix well with my learning style. It wasn't until university that I realized the importance of real world application in math problems for me. Once I could envision a real-world situation (biomechanics) I found it a lot easier to reason problems out, rather than try to memorize a step by step process. I hope this math course can teach me many different routes to teach all kinds of different learners and help them to not find math so difficult!