May 4, 2015

## Outline

1: Three questions

2: Self-regulated learning

3: Examples of SRL and Calculus

4: Calculus activity makeovers

# Three Questions

## You might be college-ready if you

Direct and control your focus and behavior

Observe and monitor thoughts, actions, and emotions

Maintain and reinforce motivation for doing the task

Bring yourself back to the task if you lose focus

Are aware of how well you are performing the task

# Self-Regulated Learning

## Self-Regulated Learning

SRL is an ideal framework for defining and measuring college/career/life readiness.

## Areas of regulation

Cognition (thinking skills and processes)

Motivation/Affect (perceptions and beliefs)

Behavior (efforts and actions)

Context (environment and surroundings)

## Phases of regulation

1: Forethought, planning, activation

2: Monitoring

3: Control

4: Reaction and reflection

Pintrich, P. "A conceptual framework for assessing motivation and self-regulated learning in college students", Ed. Pysch. Review 16(4), 2004

## What we know about SRL:

SRL enhances student performance and achievement

SRL enhances the amount and depth of learning (Jensen, 2011)

SRL predicts SAT scores more strongly than IQ, parental education, or parental economic status (Goleman, 1996)

Ability to accurately self-reflect strongly correlates with actual achievement (Kruger and Dunning, 1999 and 2002)

SRL is neither explicitly taught, nor widely developed even through graduate study

# SRL in the Calculus Classroom

## Guided Practice

Overview

Learning Objectives

Resources

Exercises

Sample for intro lesson on second derivative

## In class:

Draw the graph of the second derivative of this function:

• What are your goals? What do you need to remember before starting? How much time/effort do you expect will be needed? How hard is this task? How might this task be applied to a real situation?
• Can you describe your thought processes? Are you working and thinking effectively?
• What tools and facts do you know? Are there good places to go that can help? Have you seen a similar problem that you've solved? Should you be working harder/smarter? Can you formulate a precise question for help? Do you need a break or a change of scenery?
• How would you evaluate thought processes, feelings, and environment? What was hardest and what would you do differently next time?

## Peer Instruction

The first derivative of a function $$f$$ is shown below. What are the critical values of $$f$$? Select all that apply.

1. $$x = -4$$
2. $$x = -1$$
3. $$x = 0$$
4. $$x = 1$$

## Ubiquitous computing enables:

Authentic data and research skills

Debugging (use WeBWorK and have students find/repair errors)

Problems with not enough/too much info

Compute, then check answer Build models, then evaluate model

Exercises without solutions provided

Textbooks with minimal examples provided, e.g. Matt Boelkins Active Calculus

# Calculus activity makeovers

## Compute the following derivatives:

• $$\frac{d}{dx}\left[ x^3 - x + x^{-3} + 1/x\right]$$
• $$\frac{d}{dt}\left[ \cos(\ln(1/t)) \right]$$
• $$\frac{d}{dw}\left[ \dfrac{14w}{w^2 - \sqrt{w}} \right]$$
The rate at which photosynthesis takes place for a species of photoplankton is modeled by the function $$P = \frac{100I}{I^2 + I + 4}$$ where $$I$$ is the intensity of the light reaching the plankton. At what light intensity is $$P$$ a maximum?
Compute the length of the graph of $$\displaystyle{f(x) = \frac{2}{x} + \frac{x^3}{24}}$$ from $$x=1$$ to $$x = 3$$.
Determine whether the following series converge or diverge:
• $$\displaystyle{\sum_{n=1}^\infty \frac{n^2 + 1}{n^3 + 1}}$$
• $$\displaystyle{\sum_{n=1}^\infty \ln \left( \frac{n}{n+1} \right)}$$

# Any questions?

## Thank you

Robert Talbert, Associate Professor of Mathematics

Grand Valley State University, Allendale, Michigan USA

talbertr@gvsu.edu