Two weeks ago, The Educator’s Book Club and Margie Pearse were able to host our first successful live on-line book study! During this first session, hosted on May 24, 2015, we discussed Habits 1 and Habits 2 of Teaching Numeracy: 9 Critical Habits to Ignite Mathematical Thinking. With a group of excited and dedicated teachers, it’s no wonder that the conversation deepened and we began to discuss how we each can implement these habits and improve our instruction. This is a brief summary of the discussion!
As we discussed number sense, Margie Pearse recommended some great tools for us to use in the classroom. In fact, check out her TPT store! She has some great resources for sale and for free!
Building number sense is so important for students of all ages, and we need to be mindful of their various learning styles. Providing a variety of tools to learn with is crucial, so Margie provided some great options!
She provided an example of a math rack, aka rekenrek. Personally, I have made and had these in my classroom, but I admit to not using them as often as I should have. Actually, I remember making them, but it was a shared material that I don’t think ever made it to my classroom. Either way, I could have made more for myself. There are a number of ways to make these if you or your school does not have the means to invest in any for you. I made them of foam, pipe cleaners, and beads. But I have found some great tutorials below!
Personally, I’m excited to try making them of blinds! They seem so durable! If you are curious as to how they can be used, check out this video!
How many of you have a 100 chart in your classroom? I am assuming that most of you do. I did and do. So, here is my next question. How many of your students struggle counting or skip counting past 100? I always had several students who struggled. Be careful with this. These students may never build a solid understanding until we teach them. We can’t assume that they will eventually “catch on”. This being said, Margie offered a great solution! Instead of using a 100 chart, use a 120 chart! Why didn’t I think of that!? This seems like such an obvious solution and I can’t wait to chuck my old chart and replace it! Check out this one and it’s free! Or check out the one below!
We, then, continued our conversations into developing mathematical thinking and problem solving skills. I am sure that we can all agree that this is a very imperative skill for our children to learn, but how do we do this? The first step would be to stop providing formulas at the beginning of a lesson. There is a misunderstanding in mathematics that if a student can formulaically solve a problem that the student understands the concept. In fact, this only proves that a student knows how to follow directions, and not think critically.
Instead, Margie recommends providing the students with a real world problem and have them collaborate and solve the problem with the knowledge they already have. This helps them strengthen their prior knowledge and bridge their understanding to the new material. For example, when introducing multiplication, provide a real-world problem like, “Sam just bought 4 packs of candy. Each pack has 7 pieces in it. How many pieces of candy did he buy?” Encourage the students to collaborate and problem solve. Did they choose to draw? Repeated addition? Or did they invent their own solution? When we, as teachers, observe our students collaborate and host focused discussions, we are able to deduce their true understanding of the problem at hand.
We, as teachers, do not need to be at the front of the classroom for extended periods of time. Learning best takes place with engagement and Margie provided this wonderful resource on how to improve that engagement in the classroom. She recommended using Debbie Math Work Stations. This is a great way for students self-monitor their work, collaborate, practice prior skills, and build current ones! All the while, the teacher is able to provide more individualized assistance.
Lastly, I found Habit 1 to be the most impactful. Estimation should not be it’s own unit, but, rather, it should be utilized across the curriculum. Estimation is numerical thinking in action. Teachers can determine a great deal of a student’s understanding based on an estimation and explanation. For example, if the answer to a question is 4500, but the student estimated 2, then we can assume that there is a disconnect in the student’s understanding of a concept. This applies to any math problem, not just the unit on estimation. This is also a great tool to teach students as a means to check their work.
In fact, I have subconsciously used this skill recently! I’m not sure if I can use the word estimate in this instance, but I definitely used number sense to solve my cooking problem! I was following a recipe that called for 4 parts soy sauce and 2 part mirin (a sweet rice wine). I “tastimated” that the taste would be strong with the soy flavor and that the liquid would be a dark brown. Well, I doubled the recipe, and it was neither strong nor dark. Based on my original “tastimate”, something was wrong. I backtracked and realized that I hadn’t doubled the soy sauce portion, though I doubled the mirin. Problem solved and I had no wasted ingredients!
Our students are very good at regurgitation. Most people are. But we need to prepare our students for a future we yet to know. A future full of tools yet to be invented and needs yet to be discovered.
I am so very excited to for our next live discussion with Margie Pearse that will be hosted on Sunday, June 14, 2015 at 7pm EST. Join The Educator’s Book Club on Facebook for more information on entering the on-line discussion room! Or follow @edsbookclub or @Pearse_Margie.