While our student gains in math and science over the past decade and a half are impressive, we need to address the lower percentage of students who are “advanced” in these critical subjects. Yesterday, I noted what we can do to improve the quality of our math and science teaching corps. Today, I want to focus on a number of steps we can take to strengthen STEM standards, instructional practices and assessments.
Strengthen the K-12 Mathematics Standards. Well-structured academic standards logically progress from less difficult or complex topics to more difficult or complex topics, both within a grade and also from grade to grade. We could improve our already best-in-nation math and science standards by paying close attention to transitions across specific grade spans so as to avoid repetition of topics year after year, without the expectation of closure; specifically,
Strengthen Mathematics Instructional Practices. Basic teaching principles–e.g., regular formative assessments in the elementary grades to monitor student learning and individualize instruction–should always guide teachers. But high-quality research and the professional judgment of experienced and accomplished classroom teachers can help identify ways to improve, as well as practices to avoid.
In fact, high-quality students often don’t support some instructional practices currently promoted in mathematics education. For example, it’s hard to find high-quality research supporting either wholly student-centered or wholly teacher-directed approaches to mathematics learning. Nor does high-quality research support emphases on either small group work or problems contextualized in daily life (so-called “real-world” problems).
What do we know that improves instructional practices? Here are three actions:
- • Ensure that students develop automatic and accurate execution of standard algorithms and use these competencies to solve problems. so, for example, overusing calculators might impede the development of automaticity (fluency in computation)
• Ensure that students with learning disabilities and other learning problems regularly receive explicit systematic instruction in order to learn mathematics.
• Let mathematically advanced students, who can learn mathematics faster than students proceeding at a normal pace, do so.
Finally, we need to strengthen the state’s K-12 math assessments. There are many ways to improve the MCAS math assessments, but let’s again stick to three:
- • In PreK-6, assessments should give more prominence to immediate recall of number facts. Immediate recall frees the “working memory” for solving more complex problems; e.g., the times tables are needed to execute standard algorithms automatically. Such an emphasis will ensure that students gain the capacity for more complex mathematical concepts over time.
• In PreK-8, assessments should give prominence to patterns, including algebraic patterns.
• Keep math assessments mainly consisting of multiple-choice questions. Removing short-answer questions from the Mathematics MCAS at all grade levels would lead to modest cost savings and faster delivery of test results, but, more importantly it would provide greater objectivity in scoring. Contrary to frequent claims, constructed-response format questions, especially the short answer response, do not measure different aspects of mathematical competency (or more authentic mathematical skills). If we want to demonstrate knowledge acquisition in a broader context, we should retain the open-response portions of the tests.
Given the multi-year, $143 million commitment already in place to create MCAS tests for Massachusetts, this can be quite easily inserted into the future year tests. If we join the “national standards”, all of the actions noted above on standards and assessments will have to go through national committees and the federal bureaucracy. To the Governor and Commissioner and Secretary of Education: Thanks. We’ll have really good luck with that, I am sure.