The pandemic has prompted administrators, coaches, and teachers to re-examine their priority standards, the Multi-Tiered System of Supports (MTSS) framework and evidence-based practices. Here are a few resources recommended by the Grant Wood Area Education Agency math team that are “go-tos” for math standards and evidence based practices.
These shifts in mathematics encourage educators to look at focus, coherence and rigor and consider how they all work together within a MTSS framework.
|DuFour’s PLC questions||Think Abouts
(based on Return to Learn Coaching Protocol)
The Common Core and other college and career-ready (CCR) standards call for a greater focus in mathematics. Rather than racing to cover topics in a mile-wide, inch-deep curriculum, CCR standards require us to significantly narrow and deepen the way time and energy are spent in the math classroom. Focus deeply on the major work of each grade so students can gain strong foundations, solid conceptual understanding, a high degree of procedural skill and fluency, and the ability to apply the math they know to solve problems inside and outside the math classroom. (Achieve the Core)
The FOCUS BY GRADE LEVEL documents along with the Widely Applicable Prerequisites for High School are great places to begin when revisiting math standards.
Focus is at the heart of the standards. Without it, educators spend too much time “covering material” instead of teaching the major works of each grade level/ course. At any level of instruction (universal, targeted or intensive), teachers should understand the concepts and skills in which their students need to be proficient. Focus helps teachers target their instruction for their students. The same philosophy applies to intervention at all tiers of instruction, including special education at all levels. The Content Guides in UnBoundEd give further guidance around the major concepts and skills at each grade level. In addition, PARCC Model Content Frameworks for Mathematics is especially helpful for grades 3-11 while Appendix A is especially helpful for high school.
Thinking across grades: College- and career-ready standards are designed around coherent progressions from grade to grade. Learning is carefully connected across grades so that students can build new understanding onto foundations built in previous years. Each standard is not a new event, but an extension of previous learning. (Achieve the Core)
Linking to major topics: Instead of allowing additional or supporting topics to detract from the focus of the grade, these concepts serve the grade-level focus. For example, instead of data displays as an end in themselves, they are an opportunity to do grade-level word problems. (Achieve the Core)
The COHERENCE MAPS in Achieve the Core enable teachers to link grade level standards to standards above and below grade level. This is especially helpful when thinking about assessments and tasks for standards at any MTSS tier.
When students are below grade level, it’s critical for all teachers (general education and special education) to understand the coherence of the standards. The progression of the standards enables educators to scaffold instruction and intervene to make grade level content accessible to all. Using various forms of assessment (screeners, diagnostics, formative and summative) leads to making data based decisions about students, which, in turn, leads to more effective instruction and proficiency. The 2018 Kansas Mathematics Flip Books provide clarity about the meaning of the standards and include the Mathematics Teaching Practices, an in-depth look at The Standards for Mathematical Practice, instructional strategies, and resources/tools to support equitable learning opportunities for all students.
Means to “pursue conceptual understanding, procedural skill and fluency, and application with equal intensity.” (This is different from the dictionary meaning of rigor.)
Conceptual understanding: CCR standards call for conceptual understanding of key concepts, such as place value and ratios. Students must be able to access concepts from a number of perspectives so that they are able to see math as more than a set of mnemonics or discrete procedures.
Procedural skill and fluency: CCR standards call for speed and accuracy in calculation. Students are given opportunities to practice core functions such as single-digit multiplication so that they have access to more complex concepts and procedures.
Application: CCR standards call for students to use math flexibly for applications in problem-solving contexts. In content areas outside of math, particularly science, students are given the opportunity to use math to make meaning of and access content.(Achieve the Core)
Look carefully at the math standards. Does the standard mention objects, pictures or symbols? Does it speak of fluency or application? The standards inform about the rigor using words such as estimate, interpret, represent, evaluate and apply. Check out this resource from ANet for further approaches to increase the rigor of mathematics instruction.
Another great site for addressing accelerating learning and increasing core instruction can be found at the TNTP website.
Instructional tools and strategies are needed in order to be effective math teachers as outlined in Principles to Actions (NCTM, 2014). Here are some resources for evidence based practices teachers can use to increase the productivity of their mathematics instruction,
- Teacher Education by Design Many have seen this site when math consultants teach about number talks and instructional routines. However, there are other strategies here that promote effective instruction.
- Kentucky Center for Mathematics Resource Page This may be less familiar to some, but has a wealth of information and evidence based tools.
- National Center for Intensive Intervention has six guides to explore evidence based resources and lessons. The six areas are: Number System Counting, Basic Facts, Place Value Concepts, Place Value Computation, Fraction as Numbers, and Computation of Fractions.
Resources for Three Act Tasks:
- The Learning Trajectories is a website filled with activities linked directly to the learning trajectories for the development of mathematics ages birth to 3rd grade. Each activity considers how children learn and think mathematically while including the CRA approach when appropriate.
- CRA Approach Students are at one of these three levels of learning: concrete, representational, or abstract. By using all three levels when teaching, math can be accessible to all learners!