"Many parents and educators believe that students should be taught as they were taught, through memorizing facts, formulas, and procedures and then practicing skills over and over again (e.g., Sam and Ernest 2000). This view perpetuates the traditional lesson paradigm.” (pg 9, Principles to Actions, NCTM 2014). 

It didn’t work then and it doesn’t work now. Almost no adults in our country can do beyond elementary math procedures comfortably. As a nation, our math scores lag behind our peers. Most of us memorized procedures. Few of us learned mathematics. We need a new approach. 

Internationally, the countries that are most successful in mathematics have adopted a comprehensive approach that includes consistent frameworks, structures, and language across schools. Within the EL Education partnerships, each of our most successful schools have similarly adopted a comprehensive approach. This is not the same as adopting a published curriculum; it is a commitment to coming together as a whole school to approach mathematics instruction with the same vision, understanding, language, and practices. 

As stated in Core Practice 15, comprehensive mathematics instruction is made up of three main components:

1. Conceptual Topics 

2. Foundational Math Facts 

3. Problem Solving Skills 

A successful school’s approach will include frameworks for teaching all of these. Additionally, schools will build into their daily schedule, structures that support the high-quality implementation and assessment of these frameworks. Finally, schools will also work to ensure that all classrooms use consistent language that allows for an equitable and clear experience of learning for all students. Without these three, many schools struggle with inconsistent quality across classrooms and an incoherent learning experience for students.

EL Education’s highest achieving schools in mathematics have all adopted their own version of these three components. Below are examples of the Frameworks, Structures, and Language that these schools use. Ultimately, the specifics of these components (and even whether they are 3 independent components or whether they are presented under one plan)  are less important than community buy-in to the plan. School leadership must be committed and ideally, the full school faculty must embrace these components, customize them and use them effectively. The examples below vary and overlap, but will hopefully provide food for thought as your school grapples with creating the structure that best suits your environment.  

Frameworks: 

The Framework is the compilation of structures which define “how” math is taught at a given school. It should be chosen as part of the vision work (see Recommendation #1). A school may use more than one Framework in creating their overall mathematical approach to achieve all points of pedagogy. See “Balanced Math” below for an example of a mix of frameworks. 

• Workshop 2.0 

• LEDS Lesson Structure 

• CGI: Cognitively Guided Instruction 

• DMTI: Developing Mathematical Thinking 

• Problem Based Tasks

• Balanced Math 

• Dan Meyer 3 Act Tasks

Structures: 

Structures are just what they sound like: routines and activities that provide the scaffolding on which the math learning is built.  Below are some examples of the types structures your school may consider implementing:

• Intervention structures

  • Ex: BOA: Beginning, On Target, Advanced (Tiered Intervention)

• Number Talks and other mathematical routines

• Mathematical Discourse Structures

• Common Planning Structures

• Common co-teaching structures across a school 

• Differentiation structures (see Recommendation #8 for more ideas)  

• Remote Learning

Language: 

Consistent use of language across classrooms is crucial to ensuring consistent (and equitable) results for all students.

• Language use should be planned as a school. The team should define commonly used terms that align to the school’s vision of mathematics instruction. If choosing a common curricular tool (say Illustrative Mathematics or Eureka math), work must be done to highlight and unpack commonly used terms, however the tool can serve as a guiding tool for this. 

• The particular vocabulary chosen does not need to be consistent across schools. Different EL Education schools may implement different language to address differences in environment and school culture.   

• See here for a cumulative resource on norming mathematical language. 

1. Ensure school has adequate TIME built into the day for teaching mathematics. Ideal is 90 minutes per day (especially for schools that have a wide range of student needs that would require a range of intervention blocks). 

1. • This time can be garnered through: 

     • Ensuring a daily 90-minute block (which allows for a grade level curriculum to be taught with additional time for intervention and extension); 

     • OR working with Science classrooms to embed and share standards across the two disciplines (makes a great deal of sense in Middle School content especially); 

     • OR ensuring an additional intervention and extension block daily and/or weekly for students to have additional time for practice, feedback, and application.

2. Ensure school has adequate TIME built into the day/week for planning mathematics instruction.  Ensure math (and science) teachers have time and the necessary tools and support to build their pedagogy and content practice. (see Recommendations #5, Recommendation #6, and Recommendation #10).