The content of a mathematics program is one factor within educators’ control that has a demonstrated positive impact on student learning.
The selection of high-quality content is therefore critical, and the process used to evaluate that content must be comprehensive. This helps ensure that students have access to the learning experiences necessary to advance their mathematical development.
Different processes exist to evaluate mathematics content. There are even third-party organizations that offer reviews of programs and content. Unfortunately, many of these reviews and processes have a limited focus on a program’s alignment with a particular set of standards. They don’t examine programs in their entirety as integrated learning systems of instruction that support teaching and learning.
Although alignment to standards is necessary, it is insufficient when evaluating the overall quality of a program’s content and its impact on student learning. As math educators, it is critical to look beyond alignment and dig more deeply into the instructional design and mathematical tasks.
Who Is Doing the Mathematics?
High-quality math content sparks student learning and engages students in investigating and discussing mathematics with the teacher and their classmates so that students develop a deep understanding of essential concepts. Traditionally, math students passively watch the teacher carry out procedures and then practice those same procedures. Effective mathematics content moves students from simply watching the teacher do math to the students doing the math themselves.
High-quality math content has developmentally appropriate but cognitively-demanding tasks that engage students in complex thinking—tasks where the solution path is not explicitly known or predictable—and that require students to explore and understand the nature of mathematical concepts or relationships. Effective content requires students to self-monitor their own learning process, deal with challenges, and access relevant prior learning; encourages a learning-focused mindset; and supports students in experiencing success.
Is the Content Balanced?
Mathematics content has traditionally focused on either skills and procedures, or concepts and problem-solving. Content should be balanced; students develop proficiency in skills and procedures based on a foundation of conceptual understanding. They then draw on their understanding and skills to reason and solve problems they have never before seen.
But strong content does more than simply offer a collection of procedural, conceptual, and problem-solving lessons. High-quality content—content that develops students’ ability to be knowers and doers of mathematics—intentionally connects students’ conceptual understanding and skills through engagement so students understand why procedures work and can use them flexibly, solve problems, and recognize whether the results they produce make sense and are reasonable.
Is the Content Research-Informed?
Much is known about effective mathematics teaching and learning, and research-informed instructional strategies are summarized in the National Council of Teachers of Mathematics’ 2014 publication titled “Principles to Actions: Ensuring Mathematical Success for All.” High-quality content has an intentional lesson design that engages teachers and students in mathematical practices and the following instructional strategies:
- Establishing mathematics goals to focus learning
- Implementing tasks that promote reasoning and sense making
- Using and connecting mathematical representations
- Facilitating meaningful discourse
- Posing purposeful questions
- Building procedural fluency from conceptual understanding
- Supporting productive struggle
- Eliciting and using evidence of student thinking
How these strategies are leveraged in the content is more important than their mere inclusion. For example, how questions are posed in the content can have a significant impact on how students see themselves as learners of mathematics. If all the questions in the content are procedural, with a focus only on obtaining the correct answer, then students may come to see mathematics as merely a search for answers and not something to really understand.
More importantly, if students experience frustration when being asked to do more than simply finding answers quickly and correctly, they may come to view themselves as incapable learners of mathematics. Effective content helps students see mathematics learning as multidimensional and as a subject in which they can experience success and enjoyment through engagement, effort, and perseverance. In short, high-quality content can allow students to focus on learning math rather than simply performing.
Teachers as Learners
Finally, high-quality content does not ignore teachers. In an integrated and comprehensive learning system, teachers experience professional growth opportunities through tools such as classroom videos. They work with the content and grow in their own understanding of mathematics content, mathematical practices, and instructional strategies.
Learn more about HMH’s new learning programs for K-12 students, including Into Math.