Example implementation reports

The GeoGebra file featured in the gif above was created by past participant Anne Wolkowitsch

I then removed those equations and put up the following lines and equations: y=2x, y=2x+2, y=2x-3. I again asked questions to check if the students’ responses were the same as for the original set of equations. With the 2nd group of equations I concentrated on getting answers from those who tended to ‘opt out’ with the initial questions. I then followed up with the question, ‘What would they expect to see from y=-x, y=-2x, y=-2x +2; and why did they expect to see that?’

I asked ‘what would they call the point/no. which sits on the y axis? Is there an advantage to having a label for this no./point? Also, what about the number in front of the x?’ It took some prompting but I was happy with their thought processes. Some recalled hearing the term y intercept and gradient and they all then gravitated to that.

I asked them to consider ‘why’ I was having them draw the line for the equation without creating a table. One of my favourite responses was “Because it takes less time and Mathematicians are always looking for shortcuts.”

We then moved into giving the y intercept and gradient and I asked them to draw the line, then construct an equation. Some flew through this, but of course some others needed more prompts. A no. of mini lessons occurred.

Students were also given the line on a Cartesian Plane and asked to find the y intercept and gradient and then to create the equation as a flip on the previous activity.

Most students were able to understand the concepts of linear equations, gradient and y intercept and quickly applied their knowledge to new situations. I also used this method when graphing parabolas; showing examples, comparing, discussing and then creating expressions. When it came to (x=3)2, I only showed them one example on Geogebra with the equation and asked them to consider where the parabola would be for (x-2)2 . The students had to prove to me that their answer was correct and then create their own example. I also had an extension activity of examples such as (x-2)2+3. These last 2 activities were intended as ‘brick wall’ strategies. I encouraged peer discussions at this time.

Student spread is considerable in my Year 10 classes, but I find that asking question of the students, giving them the opportunity to discover the answers really helps in their understanding and retaining of the concepts. As discussed earlier, I am happy to incorporate mini lessons as I feel this helps keep all students engaged and progressing rather than me stopping and starting the entire class. We do of course have ‘come together’ sections. I find I have to be very prepared with the challenging extension work for those students. Unfortunately I don’t always have enough of these tasks and it is an area I am working on.

Tracy Pearson, St Mary MacKillop Catholic College Isabella Campus, May 2016

They further factorised the equations to find out the solutions. Brick wall , mini lessons, socratic questioning are being used regularly in my lessons. I am doing representation of data with year 8 students. I got them to do a survey to find out their favourite animated movie.

I then got them to construct a divided bar graph on a 30 cm long strip of cardboard. The divided bar graph was then joined at the ends to make a circle. The students then placed it on their books and drew a circle and using the markings on the divided bargraph, made the sectors in the sector graph. The divided bar graph was then cut into sections and then pasted in their books as a column graph. The students enjoyed this activity and they were able to understand that the same information can be represented in many ways - divided bar graph, sector graph and column graph in this instance. I did this activity rather than use the textbook to do this topic in class. The textbook questions were given as homework for the weekend.

Gousia Naeemullah, May 2016

From the coordinate geometry workbook I had the idea to try a similar approach to teaching parabolas, exponentials, hyperbola and circle graphs. I have created a, first attempt, workbook for students to learn about parabolas, though, will not be able to test it on my year 10 class until after this course has finished. I used my interpretation of the structure of the coordinate geometry booklet, being more fluid and student directed, to create my one, with some interactive GeoGebra files to aid in explaining different transformations.

I have attempted to take elements of the different strategies to help students learn about graphs in a more natural and explorative way.

Enjoy the attached workbook and files on parabolas. I know I have enjoyed making them.

Naomi Aigner St Mary MacKillop Catholic College Isabella Campus, December 2015

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