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 – firstname.lastname@example.org
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