Having a systematic and sequential curriculum is key to all subjects but maybe most critical in math. What we have learned through time is that there are some key concepts that we must build students up to. When the MA Standards in Math were revised in 2017, these concepts were clearly highlighted and often thought of as "gateways" that can be achieved with some key shifts in our curriculum and instruction. The key shifts are:
1) Greater focus on fewer topics
2) Coherence through the grades
3) A focus on conceptual understanding, procedural skills and fluency, and application
While it may seem like so much is covered, the shifts are meant to actually make it simpler and more coherent. Mastery of the prior concept is seen as a "gateway" to the next. Not that we must achieve mastery before moving on, in fact we want to continue to advance students through curriculum, but we do know that we should focus our attention and instruction on these key aspects in certain grade spans. Kindergarten through 8th Grade can be summarized as such:
In grades K–2 we focus on building math fact fluency with addition and subtraction and problem solving through an understanding of the base ten system.
In grades 3–5 we shift to multiplication and division fact fluency of whole numbers and fractions while also applying it solving problems.
There is a noticeable shift in grade 6 to focus on relationships between numbers with ratios and proportions and representing them with early algebraic expressions and equations.
By Grade 7 we are expanding our understanding of ratios and proportional relationships, and arithmetic of rational numbers.
In grade 8, we begin our study of linear algebra and linear functions but this is not yet considered Algebra 1.
This is the district's 4th year implementing Eureka from Great Minds as our core K-8 mathematics program. This curriculum places a focus on these key shifts and provides the district with a coherent math curriculum. This is critical, as prior to this, students received very different math instruction from each school and it had little vertical alignment by grade level. The curriculum places a balanced emphasis on building fact fluency and application of the skills to solve problems. The skillful implementation of this curriculum recognizes that students will be able to more effectively solve problems when the understand the "why" of how numbers are constructed and deconstructed. Giving visual models and different ways to represent numbers, promotes student understanding from a conceptual standpoint and not just a memorization or procedural standpoint.
Of course a coherent math curriculum does not stop at 8th Grade either. As we prepare students for Algebra through Eureka, we have also adopted the Pearson Savvas enVision program for Algebra I, Geometry and Algebra II and this is now our 3rd year using this program. We often refer to this course sequence as AGA and enVision provides us with that coherent and flexible program to engage students. Typically students begin this sequence as Freshman in High School and it generally dictates the next three years of math study with flexibility for students at the Honors level and for those who may need adaptive support. We also recognize that some students are ready for more intensive study of math at an earlier grade which is where we implement a Compacted Math curriculum at Grade 7 for those students who have demonstrated a competency and readiness for an early start with Algebra I. The Compacted Class advances students through the standards covered in Grade 7 and 8 in one year and prepares them to begin the Algebra I class at the Honors level while in 8th Grade. Having flexible pathways is an important feature for our schools and district because it provides us opportunities to advance students through math courses taking more rigorous and challenging math classes throughout their High School experience.
The AGA program with enVision is a "Model and Discuss" program. The digital version of the text provides many adaptive features with opportunities for students to have repeated practices but also to see and use solutions as a way to fully understand the concepts. This can be a shift from instruction previously that was largely focused on "procedures" rather than conceptual understanding which promotes application in a new opportunity. Furthermore, our teachers are utilizing the curriculum tools to teach students to intentionally choose from alternative algebraic strategies when solving problems which has shown to be a very effective approach to boosting student understanding of concepts and application of those skills.
Like with any curriculum shift, the skillful implementation can take time to develop. Our teachers learn more each year about how best to raise the rigor and expectations we place on our students, while also supporting them through some "productive" struggle. Use of data helps drive our instruction and planning. Our math data meetings help our staff look at bigger picture areas to help focus our instruction but also provide focus for specific students and areas they may need instruction with.