We refer to these changes we are seeing in our math instruction as an "instructional shift" toward greater

*understanding*, moving beyond teaching isolated procedures that are easily forgotten. By asking students to explore more than one strategy, critique others' thinking, and write about their own mathematical thinking, we are giving them greater opportunities to understand the math that they use in their problem solving. For a little more on "teaching for understanding," here is a recent blog post with an interesting example of looking at

*using multiple strategies*from David Ginsburg via EdWeek:

Ginsburg's example of looking at two distinctly different ways to solve a problem is one way to "construct viable arguments and critique the reasoning of others," and it helps our students "make sense of problems and persevere in solving them." Almost all of the CCSS Standards for Mathematical Practices (SMP's), in fact, relate to this example.

A successful mathematics program requires research, drafts, revisions and trials. There were years when I taught my own custom-designed lessons, and was it ever frustrating how many of my seemingly great lesson ideas flopped, and flopped hard! Sometimes what I thought was fun and engaging turned out to be embarrassing or boring to my students. I had a difficult time deciding how much homework to assign, how long to stick with a concept when my students are not demonstrating mastery, how to differentiate, and how often to incorporate group and partner work into my lessons. I was proud of the home-made lessons that had succeeded, but the many late nights of planning and organizing had taken its toll.

When my district offered to give me a published math program to teach the next year, I was humbled at first, but eventually I welcomed the lessons, scope and sequence, pre-made assessments and professional development that came with it. It did not feel like a defeat! It felt like a revelation.

I realized that while a curriculum designed by mathematicians at a big university and published by some large profit-seeking corporation may not be everything I, personally, want them to be, I have the expertise and experience as a teacher to deliver them effectively, and not feel as though I am sacrificing my instructional integrity and creativity. In addition, the lessons I designed, no matter how hard I tried to diversify them, tended to reflect my own teaching styles and preferred strategies. In other words, I didn't do a very good job of incorporating all of the SMP's into my instruction.

So this brings us back to Everyday Math, the McGraw-Hill published program we use as our K-6 math curriculum. In its new incarnation, it is designed as a Common Core program, which is to say, all its lessons and units were designed to teach the Common Core State Standards for Mathematics, including the Standards for Mathematical Practice. The program spirals, which is to say it teaches concepts continually throughout the school year, and the kindergarten to sixth grade span of years.

The spiral concept seems to have come slightly under attack in some of the discussions and readings I have come across. Older editions of Everyday Math have been criticized for not diving deeply enough into concepts before jumping ship and switching to a completely different concept, sometimes leaving students without a deep enough understanding of what was taught. By the time the concept "spirals back again," some students require total re-teaching, while others retain enough to take their understanding to a new level.

In reality, almost every math program that spans more than one or two grade levels also spirals its content. The Common Core itself spirals its content. One major difference between the old Everyday Math and the new Everyday Math (EM4) is that the spiral now (more or less) parallels the spiral of the Common Core, teaching specific content within specific domains every year. In earlier professional development this year, we looked at how important place value is throughout different points of the K-8 span. It appears in the Common Core standards many times, and it shows up in the EM4 curriculum many times as well.

Another major difference with EM4 (which we have addressed before and will continue to address again) is that it places a much greater emphasis on the teaching and learning practices outlined in the Common Core Standards for Mathematical Practice. In two years' time, third grade teachers will notice a big difference in their students' abilities when it comes to writing about their mathematical thinking. Students in first and second grade are already becoming far more versed at using diagrams and words to describe

*how*they found the solutions to their problems. And kindergarten students are sharing more of their thinking out loud and are learning how to communicate their mathematical thinking as well.

Teachers of Everyday Math are often asked to "trust the spiral," but I think the better way to look at it is to

*understand*the spiral, to

*know that it is there*. What our students are experiencing now is going to help them with their learning weeks, months and years from now. This is true both with regards to the content standards and the standards for mathematical practice. The place value lessons they get now, whether or not they completely master them 100%, will help them with their addition later in the year, and their ability to manipulate data next year, and their work with rational numbers two years after that. Likewise, the oral communicating they are doing in kindergarten math lessons will help them to express themselves on paper in first grade, which will help them become more confident with problem-solving tasks in third grade. In the end, we will see far more students demonstrating greater understanding of the math they are doing, and showing greater confidence in their solutions. Fewer students in sixth grade, when faced with the task: "Explain how you know your answer is answer is true," will respond with exasperation and fear.

Finally, when it comes to teaching a math curriculum like Everyday Math, it is best to look at the curriculum as a presentation of math concepts (standards) put together by expert mathematicians that

*you*will be collaborating with by teaching it! In fact, we are all collaborating together, for when we see something in Everyday Math we don't understand, or don't like, we seek each other out to make sense of the situation and come up with a solution. Your teaching expertise, along with the support of colleagues and myself, and the research, drafts, revisions and trials that went into the authorship of EM4, make up the collaboration needed to facilitate a unique, engaging and meaningful math learning experience for our K-6 students.

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