Differentiation Resources for Advanced Students

When differentiating for students that are exceeding expectations and are achieving higher than grade-level peers, the intuition is to accelerate students by starting work on the next grade level's standards. Instead of rushing to accelerate "vertically," consider these resources for differentiating "horizontally" for more depth and cognitive complexity within the grade level.

• Emergent Math Problem Based Curriculum Maps (Warning: Some of the linked resources may require a subscription!)

• Robert Kaplinsky's Problem-Based Lessons

• Open Middle

• Illustrative Mathematics Tasks

• 3-Act Math Tasks (K-5, 6-12)

• 5280 Math

• Math for Love Free Lessons

• Math and Logic Puzzles

• SolveMe Puzzles

Math Intervention Shouldn’t Feel Like Intervention

Remember reading groups in elementary school? It probably depends on which reading group you were in. If you were reading grade level texts and engaging in small group conversations around vocabulary and comprehension with the teacher and peers, it might have felt typical and expected. But then there was the “blue bird” group. Remember that group? Of course you do, as everyone remembers the “blue bird” group. Students in the “blue bird” group read different books, and their small group sessions with the teacher looked and felt different. Let’s just say the “blue birds” weren’t going to end the school year at the same level as the other reading groups, because their experience wasn’t exposing them to anything that resembled grade level expectations as readers.

Whether we realize it or not, we tend to do the same thing when providing intervention blocks or double-dip classes for students in math. True, these students (presumably) are also in a core math class with their peers, but what is the additional intervention time doing to help students access, succeed, and grow in that math class? And teachers that end up teaching an intervention block for the first time typically ask one of two questions right away: “What program do we use?” or “What program are we going to buy?” In response to these typical questions, here are some thoughts about designing successful intervention blocks for students:

• • Treating a math intervention block like a study hall for core math classes has good intentions, but it assumes that more time doing the status quo is going to solve the problem. While some students may benefit from one-on-one tutoring and support in a study hall setting, most students are needing a different learning environment that challenges their perceptions of math, their math ability, and math classes in general.

  • Intervention block lessons should be based on the big ideas and major concepts of the grade level; we can’t intervene on everything, so use the time to ensure students engage in conceptual understanding, procedural fluency, and applications with the essential content.

  • Get to know your students and their strengths through meaningful mathematical tasks that promote reasoning and problem solving. No student gets excited about a bunch of isolated skills practice worksheets (print or digital) from prior grades. Rich tasks with multiple entry points lead to student engagement and mathematical discourse. And don’t over-scaffold these tasks for students; allow for productive struggle. Examples of such tasks include Open Middle, 3-Act Math (K-5, 6-12), Robert Kaplinsky's Problem-Based Lessons, and Which One Doesn’t Belong?

  • No commercially-published program or digital product can support students in learning math like a highly-qualified teacher can. These students need more time with a teacher and not more time on a screen. Everyone’s worst vision of an intervention block should be the sight of students quietly working on Chromebooks/iPads with earbuds as they progress through digital lessons or practice sets.

  • Math intervention blocks should be language-rich environments with a focus on mathematical discourse, academic vocabulary, and language development. Purposeful teacher questioning fuels mathematical conversations and student thinking and responses maintains momentum. Students in math intervention may not be accustomed to having their voice and thinking expressed publicly, and this must be a norm of the learning environment.

  • While an intervention block should reinforce (and even pre-teach) concepts in the core math class, how might an intervention block be a time and space for students to wrestle and engage with non-traditional math tasks, puzzles, or games in an effort to change their mindsets and attitudes toward mathematics? Examples of such tasks include youcubed.org Math Tasks, Math and Logic Puzzles, and Cut the Knot ​​Interactive Mathematics Miscellany and Puzzles.

Math intervention is responsive instruction, not following a prescribed scope and sequence or forcing students to relive unsuccessful mathematics experiences from the past. Effective instruction for intervention must be grounded in the eight Mathematics Teaching Practices (NCTM, 2014). In addition to supporting students in their core math classes and excelling with grade level expectations and content, the goal of a math intervention block should be focusing on the promotion of positive student math identities, helping students find confidence in their abilities to understand mathematics and recognizing mathematics as worthwhile and useful in their lives.

Additional resources and posts related to best practices with mathematics intervention:

• How to Develop an Effective Math Intervention Program (Edutopia)

• Making the Most of Math Intervention Blocks (Edutopia)

• Supporting Struggling Learners in Mathematics (Colorado Department of Education)

• Minimizing the “Matthew Effect” (Mark Chubb)

• Intervention for Middle and High School with Kevin Dykema (Room to Grow Podcast)

Progress Monitoring & Intervention Resources for Grades K-8

Check out our MTSS Progress Monitoring Considerations for K-8 Mathematics

Looking for screeners and progress monitoring tools?

• easyCBM is free and reliable for progress monitoring by domain

• Acadience Math K-6 is free and best used with students identified as Tier 3 or "Three or More Grade Levels Below" on the i-Ready Math Diagnostic

• Forefront Education also has some free K-6 interview-based number sense screeners that can also be used for pinpointing conceptual gaps with number and operations

Looking for math intervention resources available to all St. Vrain teachers?

• Elementary: enVision Mathematics K-5 lesson Reteach to Build Understanding pages and the Intervention Activity in the Teacher's Edition; Math Diagnosis and Intervention System; i-Ready Tools for Instruction

• Middle School: enVision Mathematics 6-8 lesson Reteach to Build Understanding pages, Additional Vocabulary Support pages, Build Mathematical Literacy pages; Math Diagnosis and Intervention System; i-Ready Tools for Instruction

How about additional intervention tasks and activities you can use with students?

• Colorado Department of Education Math Intervention Toolkits

• Georgia Numeracy Project Tasks and Activities (aligned to Georgia Standards of Excellence)