The Common Core Learning Standards and the modules that were written to support those standards in New York have shown me new ways of helping students become real mathematicians. As a former middle school math teacher, I saw students come with either a love of mathematics or a deep “I just can’t do math” attitude. I also had colleagues and friends who would readily admit their dislike of mathematics, but never say they hated reading! I could never understand how one could dislike a content that I loved. Over my teaching career, I often looked for ways to help my students get to know math and to love it. But what was it that made so many students math-phobic? I have decided it was because we were taught the “how” of doing math – like “flip the second fraction and multiply” or to “FOIL” – instead of the “why”. I’m not saying that learning the mnemonic isn’t valuable or that we should throw out all algorithms, but we should peel back some of the layers and help students discover them at a much deeper level than we’ve ever had time or support to do.
As part of our work as the Network Team, we have had the opportunity to explore a number of strategies that I wish I had known when I was a new teacher. While it would take me days to describe all of them to you, and I know others will probably describe them more fluently than I, there are a few that I’ll highlight because I think incorporating them into your math instruction would have a great impact on your students’ understanding of mathematics.
Tape Diagrams, also called Model Drawing or Bar Modeling, can be used to solve almost any real-world word problem by representing the problem in a visual way. This pictorial representation of a word problem, a visual reference for students, bridges the gap between the concrete (hands-on approach) and the abstract (the algorithm). Everything known from the problem is drawn before any calculation takes place. The use of tape diagrams can begin as early as first grade for simple problems such as “Marnie has 5 apples and Jaime gives her 2 more. How many apples does Marnie have altogether?” and can continue into high school with problems such as “Mike bought 6 pounds of fudge. He gave the cashier $d and received $4.26 in change. How much per pound did the fudge cost? Express your answer in terms of d.” It’s easy for most of us to jump right to a numerical or algebraic solution. But for every one who struggles to decipher the problem, drawing puts everything in a picture to give the student clues for solving. The two problems above might look like these:
The use of White Boards or Response Boards is not a new idea in the field of education, but I think their use has renewed popularity for formative assessment and the Common Core. A simple white board can be crafted for each student by placing a white piece of paper into an acetate sleeve. Use another piece of colorful paper on the other side. Students can show their answers when problems are posed so you can scan the room quickly and get a sense of which students need more support or are ready to move on. Students can slip in a template, such as a place value chart or hundreds chart, as needed, and can continue to work out solutions that can be easily erased before the next problem. There are lots of varieties of white boards: presentation notebook (with sleeve on front), dry erase boards (from hobby stores), chalkboards…the type doesn’t matter. What matters is that each student has one to use so you can quickly view the work during your lessons. This type of assessment is valuable to students in elementary, middle and high school classrooms. And, it’s GREEN!
For more information about white boards, see TeachHub.
Sprints are not just fancy mad-minute challenges. Sprints were invented by Dr. Yoram Sagher and will help to develop student automaticity with previously learned material in adrenaline-rich, motivating classroom experience. Each step of the Sprint process has a purpose, so it is important to follow specific steps when administering Sprints. The steps include embedding some type of movement in between the administration of two sprints. The movement is very similar to the “Brain Gym” movements that were introduced to many area educators a few years ago. Teachers often need to deliver Sprints on previous grade level topics, so that they fill in missing foundational pieces of their students’ mathematical development. This helps build students’ confidence and develops a foundation for them to learn new content. Then, as new concepts are mastered, they begin weaving in Sprint topics from their grade level. If you have not tried a Sprint, I encourage you to watch a video and see a Sprint in action. Teachers around the area are reporting that their students love them and they are seeing improvement in many areas.
Anne Marie Voutsinas
OCM BOCES Network Team