back in the classroom

This week I was sick and unfortunately didn't make it to class. That's okay though I was able to have a great math experience at my placement with my students. They are on the unit which involves the boundary of the circle, better know as the circumference. The class had learned about circumference through conferences and using physical manipulatives and had moved on to mid point in the chapter. This was a test to see what knowledge they had gained. Before the test I was able to see how they studied which I found quite interesting. They used conferencing! The same way they had been taught. During the lunch hour some of the children stayed in order to keep the math fresh in their head and prepare for the test. they worked together to review their homework and work through some more practice problems, often asking each other questions and trying to understand each others thought processes. I thought this was awesome, and showed what kind of relationship the students had with each other.

I had the opportunity of taking the test as well, which I think I did well on. It was structured very simply, and was easy to follow along. The questions tested the skills and knowledge of the students and were straightforward and easy to follow along. Many of the questions were able to be completed or at least started by all the students in class, they were very wide based. I liked how the test incorporated multiple choice and short answer questions which involved communication and thinking. When I completed the test I was able to observe the students who were still writing.

It was really interesting to see how some people managed their time on the test. Some students could not and would not skip a question with out writing something down while others skipped the multiple choice completely. Everyone used a different strategy, showing the differentiation amongst the learners of the class.

Here is my test :) I hope I did well.

3D shapes have been around forever, will we ever understand them?

When it comes to 3D shapes, they are everywhere, but understanding them in the classroom can be difficult. That's why we used a guiding learning activity in order to complete our task. The activity simply helped us solve the bigger picture by taking us through the problem step by step and explaining the to find the little things and put it together to find a bigger answer. The learning activity used physical manipulatives like string to measure the circumference of a circle and a toilet paper roll to represent a cylinder. We first used the cylinder and dipped the ends in ink and created our circle on the paper. We used the string to find the circumference of the circle as well find the area. Then we cut the cylinder in half from end to end, creating a rectangle. Then we used the rectangles sides to finds it area. Boom you have the surface area. The problem continues getting more and more complex as the steps continue. As a pre-service teacher this activity can be a great tool when working with students. An activity like this can be used in a variety of classrooms, not just for math and the step by step thinking is a great strategy for students to grasp. Sometimes rushing to the answer is not the best idea, I would know.

The technique of physical manipulatives has been used in my placement class often. Just this week my associate teacher was using the string technique to show that circumference was simply a length and its relevance to pi. When a circles diameter is 1, its circumference is pi. This can be easily represented with the string, especially for those learners who are curious to know what the significance of 3.14... or pi is. The students had a better understand of the concepts of pi and circumference and its significance.

Another Cool Way to measure Circumference

The video above shows another cool way to measure circumference when you don't have string available. I found this way a lot easier in my opinion.

Finally I wanted to talked about distinguishing 2D and 3D shapes and why its important to use a physical manipulative or technological tool to represent the shapes. When a shape is just on a paper its often hard to distinguish, especially at the younger grades. I mean how do you represent the difference between a sphere and a circle on paper. They look almost the same. Having the physical manipulatives like having a sphere such as tennis ball or baseball versus a circle like a plate can really show the difference in shapes. This goes for all the shapes including a triangle and pyramid, it makes it easy for your learners to grasp the concepts of dimensions.

Dimensions, not the scary type!

The past week in math class we talked about geometry and spatial sense, discussing everything about two and three dimensional shapes. I considered myself pretty good when it comes to geometry, angles and special sense as I am able to relate sports and math, particularly geometry and angles. I am a sports and physical education major after all. Forgive the "Like Mike" reference but that is how I understood the difference the three types of triangles. For example, the greatest team in basketball history the 1995-1996 Chicago Bull used a "triangle" offence in certain situations. The goal of this offence was to isolate for the great Michael Jordan, moving all players to the outside so he can take it to the basket with limited defenders in the area. Now when you think about the word I just used, "isolate", does it remind you of a triangle? Yes! Isosceles triangle, the triangle with 2 equal angles and two equal sides, and Michael Jordan at the tip running the play. Once its drawn out on the basketball court it is really easy to see.

Like Mike Geometry

Now knowing the basketball offences could be a little difficult for some to understand, but the court itself also has some interesting shapes. Other sports also use some interesting shapes, take a traditional soccer ball for example. Its made of both pentagons and hexagons. Even something like a swimming pool is shaped in a prism. It is quite easy to relate different geometric shapes and different sports. Maybe students I have in my placement learn the same way as me and I will be able to relate to them in the geometry units.

Finally I liked the use of manipulatives in our geometry class. The exercise where we had to create different shapes using smaller or more shapes was great for understanding spatial sense and provides a manipulative for those learners who work better with contact. This activity also addresses the analysis of shapes, helping learners discover similarities and differences in shapes and create different groupings of these shapes.

Working in Groups!!

Today, I am going to step away from talking about what was learned in class this week and transition my blog towards what I experienced in math during my placement this past structured experience day. My students are extremely hard working and in Grade 8, and they are focused on good grades and understanding math for when the move to secondary school. Many students want to be on the "honour role" and achieve academic excellence. They are motivated. The students have an upcoming mid-chapter test on patterning and algebra, something many of the students are not too strong with. However, there are students who excel at this strand of math and are great leaders in the classroom. This is when I was able to take what I learned in math class at Brock and apply it to my classroom. My associate teacher (I helped!!!) used something called conferencing ( or similar) which was simply putting the students into groups and having them work together, creating discussion and a great learning environment.

When the students were grouped they were assigned specific questions to work on as a team, and were grouped fairly and evenly so that some weaker students had the help of the stronger students. The groups transferred there work to chart paper and posted it for the class to see. What I really liked about this method is that a lot of the time, the students were engaged, often splitting the workload, completing the question and then discussing the reasoning behind this answer. This is a great tool for a peer evaluation as they are able to see the different strategies students in the group, as well as in other groups, used to find a solution. Also, the students were able to correct each other if there were mistakes, allowing them to see what they did wrong and gain another perspective. If I had one complaint it would be that sometimes, those who understand it more, would take over, and want to finish quickly. this takes away from the other learners as they are not able to try the problems themselves, they are simply observing the other students do the work.

Overall the group work ran smoothly, they were able to complete the review questions and post their solutions on the wall as reference. Being able to see specific strategies used by the students helped me understand their learning style as well as helped the other students with differentiated solutions.

Below are some of the work that they did.