The report, Adding It Up: Helping Children Learn Mathematics, begins with a strong statement, “All young Americans must learn to think mathematically, and they must think mathematically to learn.” Adding It Up breaks down what it means to think mathematically into several strands of proficiency. These abilities are described as five interwoven and interdependent strands. The […]
Check this out! Students were randomly assigned to experience 1 of 2 conditions: Productive Failure (PF), in which students collaboratively solved complex problems without any instructional support or scaffolds; or Direct Instruction (DI), in which the teacher provided strong instructional support, scaffolding, and feedback. Findings showed that although PF students generated pictorial representations and methods for solving […]
The other day I was working with the teachers at a school who are investigating how they might improve their math instruction. We began by brainstorming characteristics of the “ideal” math lesson. I gave teachers this prompt: What does an effective mathematics classroom and lesson look like and sound like to meet the needs of […]
TL;DR Mathing is the process of students understanding math concepts. Studenting is the process of students applying that understanding to a worksheet. Both need to happen. Mathing is more important than studenting. — Let me briefly share a recent 1st grade lesson I taught to explain what are mathing and studenting and why we need […]
In my last blog post, I shared my mental model for how to teach a lesson that incorporates both student-centered inquiry and direct instruction. There are eight steps in this instructional model, but it really is three main phases: introduction, inquiry, and direct instruction. This lesson structure is very similar to the 5 Practices for […]
In earlier blog posts (this one and this one) I’ve talked about two – seemingly opposing – views of math instruction: direct instruction and student-centered instruction. There is plenty of evidence that students benefit tremendously when given an opportunity to invent/investigate their own understanding prior to formal instruction by the teacher. There is also plenty of evidence that […]
Every three years the OECD administers and publishes the Programme for International Student Assessment, better known as PISA, which evaluates 15 year-old students around the world to determine how well their education system has prepared them for life after compulsory schooling. This test is important because it allows the performance of educational systems to be […]
Whenever I feel compelled to give unsolicited advice to teachers new to the profession, I give the following three suggestions: Stay curious. Always be willing to learn new things. Stay humble. Always be willing to unlearn things you thought were true, but aren’t. Begin each day with a reminder to yourself that you really, really […]
Teachers matter. Good teaching matters. In this week of Teacher Appreciation, I am reminded of an experience many years ago… After school one day, I wandered into the classroom of a new teacher to check how her day went. I saw this on her chalkboard… After a brief chat about the answer, it was clear […]
In this episode, we continue to tackle the huge PISA report found at… http://www.oecd.org/publications/ten-questions-for-mathematics-teachers-and-how-pisa-can-help-answer-them-9789264265387-en.htm We focus on Question #2: Are some mathematics teaching methods more effective than others? Really, this episode focuses specifically on cognitive-action strategies. What are they? How effective are they? When should they be used? If you have any questions, comments, or suggestions, […]