Dean Ballard: Thank you Emily, and good afternoon everyone. Thank you for joining the … Thank you for joining the webinar everyone. Thank you, Emily. So today the essential questions that I wanted to explore today are how do explicit instructional techniques apply to both direct and inquiry-based instruction? Why is student discourse important and what are tips for generating meaningful discourse? Why is vocabulary important in math and what are strategies for building math vocabulary? And what are some easy to use differentiation techniques and how these help students?
Dean Ballard: And just by the way, just wanted to mention that I know that there are a lot more than just these four there’s more to good teaching in mathematics and just these four things. But I only have a one hour webinar here to work with and then I had to pick four things to talk about. So I chose these four, which are really important things.
Dean Ballard: Right, so let’s kick it off here, while we’re going through ideas and samples of lessons today and different slides, I want you to think about the following conclusions derived from a meta study of research around the question. What is it about teaching that influences learning?
Dean Ballard: According to the meta-analysis of research, Hiebert and Grouws concluded that two things make the biggest difference overall. And that teaching attends explicitly to concepts, to connections among mathematical facts, procedures, and ideas. And the students are regularly engaged in struggling or wrestling with important mathematical ideas. That students expend effort to make sense of mathematics, to figure something out that it’s not immediately apparent that students are solving problems that are within their reach.
Dean Ballard: Hiebert and Grouws further explained that attending explicitly to concepts means treating mathematical connections in an explicit and public way. And this can take many pedagogical forms including discussing the mathematical meaning that underlies procedures, asking questions about the ways in which different strategies for solving problems are similar to and different from each other, and reminding students that what the main point of the lesson is and how this point fits within the current sequence of lessons and ideas.
Dean Ballard: Hiebert and Grouws also state that both student centered and teacher centered approaches to instruction can provide targeted and structured activities in which students, with the teacher guidance grapple with challenging concepts and problems. In fact, providing sufficient boundaries and direction so that student learning is centered on important mathematical concepts does require some amount of teacher guidance.