Statway Research and Development • Statway Lesson Prototype • Current Distinguishing Features • Instructional Design Principles • Hypothesis and Relevant Research • Statway Lesson Pilot Protocol • Settings to Support Piloting Lessons Reserve judgment as we proceed; we’ll be applying layers as we go.
Organizing for the Session Form pairs, seated next to each other Each pair should include at least 1 Math Instructor If you have an odd number, form one threesome and pairs. Each grouping should have at least 1 Math Instructor.
Statway Lesson Prototype Documents: 1)Lesson: Intro to Scatterplots & Associations 2) Cereal Lesson (Student Handout) Task—Familiarize Yourselves with the Docs: a)Instructors: Quickly review the “Student Handout” with your partner(s) b) Pairs: Skim the “Lesson” (pp. 1-9). Instructors verbalize things that are unique and/or interesting. Mark those in the right margin.
Current Distinguishing Features *
In the “Lesson” mark the following in the left margin
A) Rich problem… page 4 Part I B) Two kinds of goals… page 1 C) Three parts… page 3, Lesson Structure D) Three approaches for Part II… page 9 E) Sequential Subtasks, Part II… pp. 6-8 F) Subtask Questions, Part II… p. 6 and 7-8 G) Dev. Math Connections… page 2
Instructional Design Principles Document: 1)Design Principles Task窶認amiliarize Yourselves with the Doc: a) Pairs: Skim the Principles. Instructors verbalize things that are unique and/or interesting. Mark those in the right margin.
Initial hypotheses (from Instructional Design principles) • Statistics provides a context for students to learn to think and reason mathematically • A focus on concepts will make it easier for student to reason • Struggling with problems is a core part of the instructional experience
Guiding Ideas of the Statway approach • Statistics – Students are unaccustomed to the topic – Novelty voids past trauma – Fresh start at reasoning
• Teaching that promotes conceptual development – Teachers and students attend explicitly to concepts – Students struggle with important mathematics
Some Sources • The effects of classroom mathematics teaching on students’ learning (Hiebert & Grouws) • Let ‘em sweat (Yeung) • What community college developmental mathematics students understand about mathematics (Stigler, Givvin, & Thompson) pdfs available – email@example.com
Community College Interviews • Interviews with developmental math students (N=30) • Findings – Conceptual atrophy – Scraps of procedures dredged from memory – Skills to reason, but do so as last resort
• Assumption: result of K-12 instruction that’s focused on procedures at the expense of conceptual understanding
Explicit Attention to Concepts • Treating mathematical connections (among facts, procedures, and ideas) in an explicit and public way • Examples – Discussing meaning underlying procedures – Comparing and contrasting solution strategies – Considering how problems build on each other or are special (or general) cases of each other – Reminding students of the main point of the lesson and how the point fits within the current sequence of lessons
Effects of Instruction that Explicitly Attends to Conceptual Development • Students receiving such instruction develop conceptual understandings to a greater extent than students receiving instruction with lesson conceptual content • Conceptual development can take many pedagogical forms • Instruction emphasizing concept development has also been shown to facilitate skill learning
Struggle • Students expend effort to make sense of math, to figure something out that is not immediately apparent • Struggle is not – needless frustration or extreme levels of challenge created by nonsensical or overly difficult problems – the feeling of despair when little of the material makes sense – brought on by simply being presented with information to be memorized or being asked only to practice what has been demonstrated
Effects of Instruction that Involves Student Struggle • Struggle results in restructuring one’s mental connections in more powerful ways • From cognitive psychology: when students struggle, they work more actively and effortfully to make sense of the situation, which in turn leads to interpretations more connected to what they already know
Published on Aug 5, 2010
Published on Aug 5, 2010
• Statway Lesson Prototype • Current Distinguishing Features • Instructional Design Principles • Hypothesis and Relevant Research • Statway...