#INspirEDmath

February 2021, Volume 29

Productive math struggle. What exactly does this mean? One could argue that students struggle daily in math class, some more than others. How will we know when struggle has gone from being productive to unproductive? At the Indiana Department of Education (IDOE), we have had time to reflect on the success of our recent book study using John Sangiovanni's book, Productive Math Struggle. The feedback we received made it clear this book had an impact on classrooms across Indiana. As a result we have done three things:
  1. Updated the Productive Math Struggle book study website to accommodate individual and groups of educators to engage in their own self-guided book study any time and at a pace that is convenient for them.
  2. Developed a FREE full day in-person workshop for summer 2021 to dig in to understanding and implementing productive math struggle in K-12 classrooms. (Virtual attendance options available.) Complete the interest form and reserve your spot today!
  3. Dedicated this month's newsletter to introduce or enhance your comfort level with productive struggle in your own classroom. Keep reading for 10 opportunities to support your journey! If you're interested in more about the tasks below, pick up your copy of Productive Math Struggle: A 6-point action plan for fostering perseverance.

Activity of The Month - The Painted Cube

Elementary

Using 1-inch cubes, Alex builds a 3x3x3 cube. Write down everything you can about this 3x3x3 shape. What do you notice? What do you wonder?


Alex then dips the cube in yellow paint. After she does this she wonders if every side of each 1-inch cube is also painted yellow. So she breaks it down into 1-inch cubes to find out. What you you think?


Find additional suggestions, including support and "push" questions for this problem on The Painted Cube resource.

Secondary

Imagine a large cube made up from 27 small red cubes being dipped into a pot of yellow paint so the whole outer surface is covered.


How many of the small cubes will have yellow paint on their faces? Will they all look the same? Provide an argument for your response.


What if it’s a 15x15x15 cube? How do you know each, without counting?


Describe the relationship between the edge length of a large cube and the number of smaller cubes painted on three faces, two faces, one face, zero faces.


Describe each relationship as linear, quadratic, exponential, or none. Write an equation for each relationship and interpret the variables and numbers in each.


View this 13-second video showing the cube being dipped for visual learners and this NRICH task for examples of student solutions.

10 Opportunities For Your Productive Struggle Journey

Productive Struggle Reflection

Before you begin your journey with productive struggle, take a step back and reflect on how you feel about the idea of struggle. From John SanGiovanni's book, Productive Math Struggle, here is a question to get you started: "What is a struggle experience you have had as a student and one you have had as a teacher? What effects have each of these experiences had on you?"

Math Identities

We all have math identities that have been shaped through our experiences with math, our interactions with teachers and learners of math, and our perceptions of math. Here is a task to help your students think about their own math identity so you can intentionally plan for struggle and respond to their needs in a way that honors their unique needs.


Math Superhero

  • Ask students, "What are you good at in math? What would be your math superpower?"
  • Provide students will large photos of themselves (or have them draw a self-portrait).
  • Students will draw themselves as a superhero by embellishing their photo with the prompt: "My math superpower is..."
  • Display the posters and refer to them especially in times of struggle.

Productive Math Community

According to the authors of Productive Math Struggle, a productive classroom community is a space where both students and teachers feel safe, respected, and appreciated for the unique contributions they bring to the collective group. Here are some characteristics to consider when thinking about a productive classroom community:
  • What norms will you establish for behavior and interactions?
  • How will you promote trust among the community members?
  • How will you build relationships taking into account the individual?
  • How will you advocate for equitable practices?
  • How will you establish a common understanding of the value in productive struggle?


Try this task to help develop your productive math community:


A Picture is Worth 1,000 Numbers

  • Students find a picture of something they value (e.g. on their device, bring one from home, draw a picture).
  • Students use numbers to describe the picture or the experience the picture evokes.


With tasks like these, you begin to learn about the student and what is important to them, allowing for connections to be made and relationships to be built.

Promote a Community of Understanding

Think about how your school values productive struggle. Do motivational posters in the hall or videos of motivational speeches come to mind? While these can be great reminders of perseverance, it just simply isn't enough. Students must be engaged in productive struggle and be encouraged to think about struggle experiences in a variety of contexts - not just in math class.


Try this task to reinforce this idea and spark conversation about productive struggle:


The Picture of Struggle

  • Display several pictures of struggle around the room or on the screen.
  • Ask students to identify the picture they think best represents their view of struggle.
  • Engage students in a discussion about why they chose their photo. Some questions to consider:
  1. Why did you choose this photo?
  2. What does it make you think about?
  3. How might the person, animal, etc. feel in the photo?
  4. Students then come together to debrief as a whole class.


This task will help you visualize how students see struggle. Do they see it as good? Do they see it as bad? The perspective of each student will shine through and give you insight to what they think struggle is allowing you to intentionally respond when they experience struggle in your classroom.

Modify Tasks to Promote Struggle

You probably already modify tasks to fit the needs of your students, but modification alone is not enough. Intentional modification with a specific goal in mind must be present. How do you modify tasks to promote productive struggle? Most math textbook problems require some form of modification to fit the needs of students whether it is to increase the rigor, be more relevant, or better align to standards. Here are some questions to consider as you are modifying tasks:


  • How does the task promote the need to think, reason, and make sense?
  • How does the task require students to think about math?
  • How does the task stay productive and avoid becoming destructive?
  • How does the struggle help? Does the struggle allow for new strategies and perspectives?

Struggle Moves

"Just-in-time Teaching" is an intentional teaching and learning strategy that is often utilized through warm ups and within tasks in the math classroom. These in-the-moment instructional moves help support students, keeping them on track to reach their learning goals. Students may struggle but laying the groundwork for productive struggle can help you plan for it and respond appropriately.


Here is a struggle move to help scaffold students as they struggle:


Catch and Release

  1. Notice: You circulate, observe students, and ask questions.
  2. Ask: When you see struggle beginning to emerge, stop the class, and ask a question relating to the struggle (this is the catch).
  3. Discuss: Students think and formulate a discussion about the struggle and get back to the task (this is the release).


This struggle move intentionally addresses struggle while helping students remain focused and engaged. It allows for the exploration of conjectures and sense-making as students debrief and discuss. Students can then use their new knowledge to see the task with a fresh perspective.

Navigating Struggle

Just because a struggle move works one day, does not guarantee it will work the next. Just like everything in our field - we must be flexible. We must continually find ways to support students in a way that works for them. Here are some tips as you navigate struggle:


  1. Revoicing - This helps others students understand what another student has said. Beware not to embellish or polish the students words. Restate exactly what they said just to clarify. You can also have other students try revoicing their peers thoughts.
  2. Helping and Holding - We want to support students and scaffold their thinking but we don't want to help too much. What is too much help? Consider these ideas as you determine if you should help or hold back. Was there enough time? Is the solution within reach? Is this a good moment for collaboration or peer support? Was tool can you suggest? Is the student on the road to destruction? Has the student exhausted all strategies?
  3. Boiling Over - Embrace the frustration. Struggle inherently creates frustration so being prepared with coping for times of frustration will only allow struggle to be productive rather than destructive.
  4. Adjust Time - Math rarely tends to fit neatly into an alloted [insert your math block minutes here] minute block. Just because you planned it doesn't mean you have to finish it in the scheduled time frame. Giving yourself grace and mercy over time will only help your students earn a much needed brain break, avoid becoming frustrated, and come prepared the next day to finish the lesson.
  5. Leverage Accountability - We all have that student that seemingly vanishes when things get hard. They sit in the shadows and let others take the lead. Try having each student use a different color pen or marker during group tasks so you can see the contributions of each student.

Student Reflection

It is not surprising the there is value in reflection. It is an integral part of the learning process. If you are using the same reflection process for every task, consider adding to your toolbox. Every task we ask our students to engage in is different, so why not ask students to reflect in a variety of ways as well? Here are three ways to reflect:


  1. Struggle Doodle - Direct students to doodle about what happened during class prompting them to think about a success, group experience, challenge, or specific moment of struggle.
  2. One Word - Build students vocabulary and conceptual understanding of productive struggle by challenging them to find the best word to express their struggle experience. Students will think of a word that captures their experience and write it on a sticky note. Students then are given time to share out to develop their ideas about the feelings, perspectives, and actions that surround productive struggle.
  3. Got It, Tried It - At the end of a lesson, students evaluate the difficulty of the task, their success, and engagement. The four categories are:
  • "Got it" - I understood the lesson and solved the problem. "
  • Didn't get it" - I had trouble understanding the lesson, wasn't able to solve the problem, and don't know what I am doing.
  • "Tried it" - I tried hard to understand the lesson and solve the problem, I tried a different strategy when the first one didn't work or I asked someone for help.
  • "Could have tried harder" - I could have tried harder and I didn't try to work through the problem.

Teacher Reflection

Not only do students need time to reflect, but teachers need it too. How are your students struggling? Why are they struggling? How are they navigating struggle? How are you responding? Here are two ways for you to intentionally reflect in and efficient and effective way:


  1. In-the-moment - You probably already keep a notebook, clipboard, or digital notepad of anecdotal day-to-day reflections. Add productive struggle experiences to your system. Record areas that seem to evoke struggle for students, tasks that seem problematic, and strategies you used to help navigate the struggle.
  2. Student Reflect, You Reflect - We know that modeling is an effective strategy used in a variety of teaching and learning contexts. Use it to reflect on productive struggle experiences. The student reflection tasks above can be used by teachers too! Promote a productive math community and build relationships with your students while intentionally perfecting your craft.

Celebration Approaches

The idea of celebration is not new and is proven to motivate students. Acknowledging student growth and perseverance will only increase students willingness to engage and spark their confidence to succeed. Here are a few ways to celebrate your students:


  1. Notice it and Reward it - Use shout out cards to acknowledge students. Teachers or students can give a shout out card. It can as simple as a notecard with the students name and the reason for the shout out.
  2. Reward Tool Usage - When you see a student use a math tool to get them "unstuck" acknowledge their decision and how it supports productive struggle.

Video of the Month

Exploring the productive struggle | Teacher Talk with Dan Finkel

FREE Productive Struggle Resources

Great Read!

Read the foreward from Productive Math Struggle: A 6-Point Action Plan for Fostering Perseverance by Matt Larson where he introduces the topic of productive struggle and why it should be used in the classroom.

Check Yourself!

The Productive Math Struggle Self-Inventory gives teachers a survey to assess where they are with productive struggle.

Look Fors

The Productive Struggle Walkthrough tool can be used for observations on teacher and student behaviors.

What is Productive Struggle?

What Productive Struggle Is and Isn't outlines how teachers can identify what is and isn't productive struggle.

Opportunities for the Field

In this FREE full day workshop, for any K-12 educator, administrator, or instructional coach, discover how to implement and support student productive struggle in the math classroom. This workshop will provide participants with key points from the Productive Math Struggle book, highlight action activities with demonstrations, and support intentional planning time. Coming this July, register today by completing this productive struggle interest form.

Presidential Award for Excellence in Mathematics and Science Teaching

The nation's highest honors for teachers of science, technology, engineering, math, and computer science is now accepting nominations and applications. This year's awards will honor those teachers working in grades 7-12. The award recognizes those teachers that have both deep content knowledge of the subjects they teach and the ability to motivate and enable students to be successful in those areas. Nominate a Teacher! Nominations are now open through March 1. Applications for grade 7-12 teachers are open through April 1. Apply today!

Help Needed: Accepting Educator Applications for Item Writing - Share with Educators!

The Indiana Department of Education (IDOE) seeks educators to write items for Indiana state assessments. This important work will take place in summer 2021. Interested educators may apply for consideration using the Assessment Item Writing Interest Survey link. Review the Take Charge Indiana Assessments flyer for details. Contact Mary Williams with questions.

Keep Indiana Learning

Keep Indiana Learning (KInL) created by the Central Indiana Educational Service Center (CIESC) provides educators with an empowering collaborative community that will transform teaching and learning resulting in relevant, engaging, and equitable learning opportunities for all students. Supported by Educational Services of Indiana, they provide resources and professional learning where educators, families, and students can connect and learn from peers across the State of Indiana.


Interested in becoming a KInL contributor? Through the GEER Grant, KInL is able to financially compensate contributors to their professional development library. Learn more about how you can be paid to contribute to KInL or contact Laurie Ferry at lferry@ciesc.org. Follow KInL on Twitter @KeepINLearning and use #KeepIndianaLearning.

Survey for Praxis Elementary Education: Mathematics Specialist Test

Educational Testing Service (ETS) Praxis Elementary Education: Mathematics Specialist test plays a role in licensure. The quality of the test relies heavily on feedback from the field. Step 1 in designing the test is defining the critical content to be measured. Please consider helping with this important work by completing this survey.

Educator Spotlight

Melissa Holden - Math Teacher - Mooresville High School

Tell us a little bit about your educational journey.


"I have always wanted to be a teacher – since I can remember that is what I always told everyone I was going to be when I grow up. Then in high school I had amazing math teachers (shout out to Denise White and Sean Galiher at Penn HS in Mishawaka!) that made me want to follow in their footsteps. They made me feel like I was capable of doing the hard things. I thought how cool would it be if I could pay it forward like that to other kids. Not just with math, but in general. That I could be someone that encouraged students to know that they ARE capable of hard things. So... I ended up at Butler University and from day 1 was declared a Secondary Education Mathematics major. The rest is kind of history. Now, today, I find myself teaching in a school building I love and have been for seven years. As well as going back to school getting my Master’s in Teaching Secondary Mathematics."


What advice would you give for teachers beginning their productive struggle journey?


"For me the number one suggestion before diving into productive struggle is to build real relationships with your students. Let them see YOU make mistakes. They need to trust you that if you put them through the wringer it is for a good reason. That there is a method to the madness. Then, you need to know what your math identity is and the identity of your students. Understand what they are lacking confidence in, and work to build that up with intentional trial and error scenarios where they can succeed. It isn’t always going to be beautiful. It may be a complete mess. But, I think that when we can turn the mess into a productive message we can learn the most from that."


If you're looking for more on discovering your math identity, check out Melissa's presentation.

Kyle Kline - Digital Learning Coordinator - Twin Lakes School Corporation

Tell us a little bit about your educational journey.


I am the Coordinator of Digital Learning at Twin Lakes School Corporation. I spent the previous five years as the Mathematics Curriculum and Technology Integration Specialist at Delphi Community School Corporation. I started my teaching career at Lafayette Jefferson High School for one year and then he spent the next 12 years at Twin Lakes High School. I have taught classes from Pre-Algebra to Precalculus. I regularly integrate Twitter (@MrKline_EdTech), flipped lessons, blended learning, and many other web tools into my daily lessons. I helped write STEM curriculum for the Indiana Migrant Education Program. This experience ignited my passion for technology education and ultimately gave me the confidence to take the leap into a different role in education. I am also a ViewSonic Authorized Trainer and a member of the Indiana Connected Educators board, an ISTE affiliate. My favorite part of teaching is the relationships with the students and helping them see that math can be fun. My main goal for students is for them to work hard to achieve to their fullest potential.


It's digital learning month! How do you incorporate digital learning into your practice and what are some resources you suggest?


"One thing that I really love doing is seeing what other teachers are doing on social media! There are so many math educators that are trying something different than the traditional approach to math AND having success with their attempts. They are engaging students, encouraging them to approach problems from different angles, and most importantly, they are listening. They are listening to students explanations and facilitating discussions with their students. I get so excited when I see a teacher posting a student math conversation on Twitter, Facebook, or Instagram.


When I first started teaching math, I thought I was the one that had to know everything and that I was the one that had to do all the talking. This couldn't be further from the truth. Jo Boaler says that a classroom discussion should be 50-50 (Mathematical Mindsets, 2015). Half of the time the teacher should be speaking and half of the time the students should be doing the talking. This is a stark contrast to how many math teachers were taught to teach math. However, times are different and so are the kids. If we really want students to be engaged in mathematics and in our classrooms, then we need to give them the opportunities to speak and to work with the math.


A few of my favorite resources that encourage mathematical discussions are easily found and FREE. Desmos, Which One Doesn't Belong?, and Open Middle are free websites that teachers can use for their classes. Activities from these websites can take anywhere from 10 minutes to an hour. It honestly depends on the way the activity is presented and how the teacher facilitates the conversation. Too many times we worry about teaching new content after a bell ringer. But what happens when a bell ringer goes over 10 minutes? Do you stop the conversation and go on to your next activity? Or do you stop and listen? Listen to the math conversations your students are having. Take yourself out of the equation (great pun there) and just listen. This is something that I will admit, I did not do a great job of when I first started teaching. Think about your classroom now. Are you the purveyor of knowledge and the only one talking? Or are you listening?"

Mathematics Educator Spotlight Nomination

We are looking for rock star math educators who are innovative and inspiring; educators who lead, learn, and collaborate with humility and passion. If you know someone (or are that someone) click the button and nominate them (or yourself)!

IDOE Mathematics Team