Questions????

Recently, I read a post by Jon Orr where he used "2 Truths and 1 Lie" as a review tool for the exam in grade 10 math and it made me think about how I could use it in my classroom. Here's my account on using "2 truths and 1 lie" in Grade 12 Calculus - what worked, what I would modify, what it showed me about my students' understanding.

I posted the function  on the board and asked my class to create 2 truths and 1 lie about the derivative of that function. My goal was to see the depth of their understanding of derivatives as well as the product rule, quotient rule and chain rule. (We has spent the previous two classes on the product rule and the quotient rule and we had covered the chain rule in this class).

I had them write their 2 truths and a lie on post-it notes and hand them in (I asked for their names on the back of the post-it and to also identify their lie on the back). My hope was to then, at the beginning of the next class, display all their post-it notes and have them as a class sort through them into truths and lies.

As I read through their responses, I didn't think the activity went that well (I did this activity in 2 classes on the same day and got the same type of results in both sections). Here are some of their answers:

One of the reasons that I thought it didn't go well was that I was not getting very detailed responses or their responses were very surface level. Most of their responses were also very similar. After debriefing the activity with a colleague, I realize that perhaps their responses showed their understanding of derivatives at that moment was only surface level. It made me reflect upon my practice - had I only focused on the algorithm and not so much on the meaning of a derivative? Was what they were producing a reflection of what I had shown them in class? If I repeated this activity as exam review at the end of the course, would I get more detailed responses?

I then questioned if this was the right type of question to ask and where might I use it to get more detailed responses. As we start the curve sketching unit in calculus, this activity may be more appropriate if when shown the equation or graph of a functions, they were asked "Determine 2 truths and 1 lie about the graph of a given function." Students would have more aspects to reflect upon and be able to create more detailed truths and lies. Would I get better responses if students were shown the equation? the graph? or both?

I also pondered using this activity as part of a conversation with students. What if I created a list of truths and lies and asked each student to identify, from the list, 2 truths and 1 lie about a function or graph and describe why they know it is a truth or a lie.

Though I was not completely satisfied with the results of the first attempt at this activity, I definitely plan on using "2 Truths and 1 Lie" again in the upcoming weeks in Calculus. The students were engaged and each student did have an opportunity to participate and demonstrate their current level of understanding.

My favourite

What is one thing that I couldn't live without in my classroom or that greatly improves student learning in my classroom? Though there are many things that I think I could choose, the one that comes to mind is Vertical Non-Permanent Surfaces (VNPS).

I discovered VNPS through Twitter near the end of the last school year.  After hearing about them from a colleague again at the beginning of this school year, I decided to try them in my Advanced Functions course and quickly discovered their usefulness and power they have on learning. I'll admit that I am a fan of reading about something (usually on Twitter) in the morning and attempting it in my classroom later that day. Some of these attempts are successful, some require some thought and reconsideration before attempting again. Using VNPS was one of these events that was extremely successful.

I usually use VNPS during a lesson that is very skill based. I have used them with polynomial long division, factoring polynomials, and basic derivatives. What normally happens is that I introduce the concept, work through some examples with the student and then have them show me their understanding using the VNPS (or I have also used them during review periods).

I begin by randomly organizing my students into small groups (usually 2 - 3) and have them move to a VNPS. I ask that each group have one white board marker for the group. The first person takes the marker and answers the question posed to the class. The group works together to solve the problem but the person with the marker is considered the lead for that question. Once each group has answered the question, the white board marker is passed to another student and another question is revealed. This continues until each member of the group has had a chance to write a solution on the board. I usually have as many questions prepared as there are members of the group.

Why do I like VNPS?
- They offer another opportunity for me to formatively see their work as well as their form in questions in a less formal setting.
- They encourages conversations between students in small groups on the concepts that we are learning.
- They allow each student to demonstrate their knowledge to the group and get peer feedback on their knowledge.
- They allow me to showcase student work within the class.