Vocabulary Decisions

By Bowen Kerins

A wide-ranging team worked together to develop the Illustrative Mathematics Grades 6–8 Math curriculum. Many of the authors were and are experienced teachers of Grades 6–8, while others are experienced high school teachers.

My own experience is as a high school teacher, then a high school curriculum writer. One of the ways the IM team’s experiences led to a higher-quality product was the discussion around language and terms used throughout the three grades. Continue reading “Vocabulary Decisions”

How the 5 Practices Changed my Instruction

I am the type of teacher you want on your teaching team. I am the person that can remember vast amounts of details, predict potential obstacles, and meet any and all deadlines.  

My organized personality is apparent everywhere in my classroom.  From classroom routines to student supplies, everything has its place.  This organization also shows through in how I plan ahead for all of my lessons. Even after 12 years of teaching, I am still not able to “wing it” when teaching a lesson. While I know my organization and meticulous planning are advantages for many aspects of my teaching, I often felt like they kept my instruction from becoming truly student-centered because these characteristics did not leave much room for flexibility. I would have a planned path for a lesson—a very specific, usually teacher-centered, way to get to the end—and never imagined I could rely on my students’ work to guide the pacing, discussion, and overall lesson as effectively as I could.  

When I was introduced to the 5 Practices framework a few years ago, I felt a missing piece of my planning and instruction suddenly click into place.  As a seasoned teacher with many years of experience in upper elementary and middle school math, I knew many of my instructional practices were high-quality, however I did not feel as if they fully came together in a way that met every student’s needs. Before I used the 5 Practices to guide my lesson planning, I found that the students who struggled to solve the math task did not fully understand that the sharing of correct solutions was a crucial part of the lesson. I also found that my students who had efficient strategies were unlikely to learn from their peers who were sharing their thinkingit was almost like since they had a to solve the problem, they felt it was unnecessary to even try to approach the problem in a new way. My students were polite and respectful, but they were not truly learning from each other. When I learned about the 5 Practices, I knew that the lesson planning structure was going to improve my teaching and in turn, student learning.

Looking back, I can see now that many of the 5 Practices were already present in my instruction.  For example, my students were used to working in small groups on rich mathematical tasks designed to draw out their ideas and strategies focused on a specific math concept or goal and I was able to predict many of the misconceptions that would naturally arise as students solved the task. However, in my planning, I was always trying to prevent these mistakes rather than use them as a learning opportunity. Students were also used to presenting their ideas in front of the class, and the audience had sentence stems to help them respond to the presenter. This is the point where the lesson usually started to falter.  The students volunteering were often the same students every time and the class did not really know how to question the presenters because most of them were still at the beginning stages of their own understanding of the concept. Honestly, I often wondered if this “student sharing” was worth the time it took.  

However, in my planning, I was always trying to prevent these mistakes rather than use them as a learning opportunity

The 5 Practices provided the structure I needed as a teacher to put all of these good teaching strategies into a cohesive teaching style that was not only student-centered but also focused on the mathematical goal of the day. As soon as I took control of the strategies being presented and the order in which they were shared, I saw a huge improvement in students’ engagement during the sharing time. Suddenly, the students presenting were the teachers, helping others make connections through the sharing of their work. I selected and sequenced their strategies in a way that moved students moved all students forward in their thinking through mathematical connections in their work.

In addition to the mathematical connections students made, there was a huge shift in how students felt about the work they did in class each day. I could see the pride in my students as they realized their thinking was not only valued, but extremely important in our classroom. Using the 5 Practices to plan before the lesson, I was able to make decisions ahead of time about things such as whether I would have students present work that included errors or misconceptions (hint: wait until later in the unit to do this!) or whether I would choose more conceptual to abstract pieces of work. Since I had a plan in place, I no longer had to hope someone raised their hand to present. Instead, I simply selected and sequenced students’ thinking in a way that allowed the rest of the class to make their own connections and deepen their understanding.  They no longer relied on me to provide all the connections for them and my classroom truly became a place where students were the center of my instruction.

They no longer relied on me to provide all the connections for them and my classroom truly became a place where students were the center of my instruction.

The 5 Practices planning framework provided me with the structure I needed to plan thoughtful and effective lessons, however it did not come without some challenges. First, finding the mathematical tasks that accomplish your mathematical goal takes time and effort. If you are not working with a problem-based curriculum, sometimes you have to comb through many resources before you find one that works. You might try a task and realize halfway through the lesson that it does not meet your goals. Two additional challenges are brainstorming the anticipated student responses alone and finding others to collaborate in this process. I have found anticipating is not as valuable in isolation as it is when done in collaboration with other teachers. In this video clip, found in full on Teaching Channel, you see my first year teaching fifth grade math in which I overcame all three of these challenges.

For the entire lesson video, visit www.teachingchannel.org.

I often did not know the task to choose, strategies and misconceptions students would have before the lesson was in action, so my lesson-planning time with other teachers became crucial to this lesson’s success. My colleagues were able to share the anticipated strategies with me and then we brainstormed strategies we would monitor for, select to share, and the sequence in which would help students make mathematical connections.      

Using the 5 Practices often requires a fundamental shift in your teaching philosophy.  This shift definitely benefits students and their ability to form their own understanding of a mathematical concept. However, it requires trust and norm-setting. You have to trust that your students will remain on task, share their thinking both in small groups and the whole class, and understand how to respond to one another’s thinking. It takes time and practice to establish a classroom culture that allows this happen on a daily basis. The 5 Practices are not an overnight success. While there are a few challenges when using the structure for the first time, these challenges  are possible to overcome and worth every bit of effort and time for both you and, most importantly, your students.

Next Steps

  • I would love to hear about lessons you are planning where the 5 Practices would support your students’ learning and help you brainstorm.
  • As you watch the video, I would love to hear about evidence you see in the video of the 5 Practices in action.
  • To see more videos from Illustrative Mathematics visit Teaching Channel.
  • Click here to learn more about professional development of the 5 Practices for your classroom or school.

The 5 Practices Framework: Explicit Planning vs Explicit Teaching

By Kristin Gray

When I first started thinking about how I would complete this sentence, analogies such as a marathon or really hard workout came to mindan activity that is exhausting, a ton of work, but ends with a sense of pride for having completed it. While these analogies were accurate representations of how difficult I think lesson planning truly is, I was continually unhappy with where students and their ideas fit into my analogy.

Planning is like putting together a puzzle.

Continue reading “The 5 Practices Framework: Explicit Planning vs Explicit Teaching”

Not all contexts have the same purpose

By Nik Doran

We sometimes use familiar contexts to understand new mathematical ideas, and sometimes we use familiar mathematical ideas to understand what is going on in a context. We do both of these things by looking for parallels between the familiar and unfamiliar structures. I want to highlight two places this happens in the Illustrative Mathematics 6–8 Math curriculum. (It’s easy and free to sign up to see the teacher materials.) Continue reading “Not all contexts have the same purpose”

Info Gap Cards: The Hidden Gem

By Sadie Estrella

May 2016 seems so long ago. I actually had to look it up on a calendar because I really thought it was more than 1.41666years ago. That was when I officially started this journey with Illustrative Mathematics. Our kickoff meeting was in Chicago. I was pumped to learn about this new adventure I was embarking on (and honestly quite scared too). One of the things I distinctly remember taking away from that meeting was this idea of an Info Gap. I hadn’t learned much about math language routines just yet but this Info Gap thing sounded really cool. Continue reading “Info Gap Cards: The Hidden Gem”

Fraction & Decimal Number Lines

By Kristin Gray

Recently, our 3rd, 4th, and 5th grade teachers had the opportunity to chat math for 2 hours during a Learning Lab held on a professional development day. It was the first time we had done a vertical lab and it felt like perfect timing as 3rd and 4th grade would soon be starting their fraction unit and 5th would be entering their decimal unit. Prior to the meeting, we read the NCTM article, “Identify Fractions and Decimals on a Number Line” by Meghan Shaughnessy, so we started the meeting discussing ideas in the article. We then jumped into playing around with clothesline number lines and double number lines, discussing what they could look like at each grade level based on where students are in the fractional thinking. Continue reading “Fraction & Decimal Number Lines”

Respecting the Intellectual Work of the Grade

By Kate Nowak

A thing that I think we did really well in Illustrative Mathematics 6–8 Math was attend carefully to really deep, important things that adults that already know math can easily overlook. For example, what does an equation mean? What does it mean for a number to be a solution to an equation? What does it mean for two expressions to be equivalent? (This is an example of the crucially important foundational understanding that gets short shrift when we rush kids through middle school math.) Continue reading “Respecting the Intellectual Work of the Grade”

Assessment Principles in Illustrative Mathematics 6-8 Math

By Bowen Kerins

A wide-ranging team worked together to develop the Illustrative Mathematics Grades 6-8 Math curriculum. As Assessment Lead, it was my responsibility to write and curate the Shared Understandings document about assessments we used throughout the writing process, and I thought you might be interested to read some of the key features.

This quote drives a lot of the ideas about assessment:

“You want students to get the question right for the right reasons and get the question wrong for the right reasons.” – Sendhil Revuluri Continue reading “Assessment Principles in Illustrative Mathematics 6-8 Math”

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