Week 7: Report and Reflection

This week our class focused on patterning and algebra. The main idea with patterns is that they represent identified regularities, in other words, we are able to look at representations in a way that we recognize that there is a regular consistency between them in order to come up with the next variant.

Some core ideas about patterns, from the textbook are:

• Patterns can be represented in variety of ways 
• Some ways of displaying data highlight patterns
• Much of other strands in mathematics is built on pattern foundation
• Algebra is a way to represent and explain mathematical relationships and to describe and analyze change
• Relationships between quantities can be described efficiently using variables

To have our students determine patterns we would look at a visual example or a stream of numbers and decipher what the pattern here is:

https://www.mydigitalchalkboard.org/portal/default/Content/Viewer/Content?action=2&scId=306591&sciId=18291

With this image, we can see the pattern is that a square is being added to each corner of the X and keeps expanded within the next steps.

But with algebra, we would decipher the formula which is a underlying way to describe what is happening in these images. So algebra explains the mathematical relationship to describe patterns. 

So the formula for the above image 4(Input) +1 = (Output). 4 is decided to be the constant because 4 squares are always added to each image. The input would vary depending on which step we are on and then we add 1 to get the output. 

So for example 

Step 1:  4(1)+1=5

Step 2: 4(2)+1=9

Step 3: 4(3)+1=13

Step 4: 4(4)+1=17

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For our activity presentations I found our presenters to be extremely well researched, this is probably one of the most complicated topics to teach, as we seen with a lot of confusion today, so it was great that our presenters were knowledgable with the topic and prepared. 

I thought that Brittany did an exceptional job modelling. The way she segued from introduction to activity was very clear and she got our minds on with questions as well as involving us in her example in which she clearly modelled how the activity was meant to be done and how it would be shown and written before she let us do it ourselves. I think this is so important because it is not always enough to teach a lesson and give an activity and have students go in without explicitly presenting what needs to be done. 

Brett should be given a lot of credit for choosing an activity which relates to maybe one of the most complicated subjects that we have come across in the class, algebra. He was knowledgable about his topic, which a good teacher needs to be when tackling a subject that confuses about 95% of the class. What I enjoyed most about his presentation was how much we genuinely learned from it as a class to come up with answers and better understand algebraic equations. For this activity we worked in groups to to determine the relationships between the input/output numbers to come up with the relationships and equations. What was strong about the activity he chose was that it fits into a social constructivist method of teaching, which emphasizes the collaborative nature of learning. I also liked the terminology he introduced with "input" and "output," and how it was laid out in the chart. I have never heard or seen algebra presented like this before and I think it makes everything much more clear and organized.

Brittany's Activity: Use the 3 questions to come up with the colours and amounts you will use to make up your pattern,
in each box create the next step to expand your pattern
[Chamberlain, 2015 (C)]

So the last part of the class we worked within groups to determine the pattern on our worksheet with the expanding X's (similar to the X pattern I posted above). In Figure 1 you will see my group misunderstood the instruction to represent the pattern change and we thought we had to come up with a way to represent it in a different way so we thought to do a real life situation with cars in a parking lot. After realizing we were supposed to show the different ways to represent the pattern within that same pattern we changed it so you will see to the right that we represented the pattern change with the change of colours and the red dots show the change.

Fig.1
Chamberlain, 2015 (C)

I chose to include Figure 2 below because I thought that this group represented the pattern in two very different ways that I would not have thought of when I looked at the pattern. It just goes to show you how very different everybody in a classroom may visualize the same pattern.

Fig. 2
Chamberlain, 2015 (C)

There are some questions I have, not about patterning and algebra, but about teaching math in general. I am always helping with mathematics in my placement because that takes up basically half of their day and I am finding out new things about different learners and coming in situations that I would like some advice on how to address.
For example...
If I am working with students on IEPs with modifications separately, and we are working through questions from the textbook but then they are making mistakes in basic subtraction. Now I have to teach subtraction within teaching another topic. That takes away from the main topic I'm supposed to teach. So what is a good strategy to approach this situation when you have to end up backtracking so far when they do not have these basic skills, without making them more confused than they already are?

How do you include students with needs like these in group collaborative activities when they are so behind?

Also, we learned earlier this semester on different algorithms but in my placement my teacher was going over the lesson topic and when I thought I knew how to solve it he stopped me and showed me the way that the school board wanted it to be taught (different algorithm). But we are learning that students should come up with their own algorithms and that there are many ways to solve problems. So I would like to know about the documents that tell us what and how we are supposed to teach our subjects.

I find that in class there is a lot of focus on the topic of the week and the reading and activities for the topic. But I hope we can include some discussions on difficult situations that will come up in our placement and how to deal with them. Especially when it comes to students on IEPs because the majority of these students have modifications and accommodations in math and I want to be prepared for how I can change my activities and lessons to be more inclusive towards them and in ways that will be clear to them.