Adult students, even at the lowest levels, have some experience with and intuition about proportional reasoning—the ability to compare two things using multiplicative thinking and then apply the comparison to a new situation. By integrating proportional reasoning throughout the curriculum, you can help your students develop important life and career skills and prepare them to tackle algebra with understanding and confidence. Proportional reasoning can be supported early on by having students explore proportional situations in a variety of contexts using concrete materials or through data collection activities. [National Research Council, p.417]. Both of these strategies also align with strategies for teaching students with learning disabilities. This course will introduce you, through hands-on exploration, both to the concepts of proportional reasoning and to concrete strategies to help students reason through ratios.
This professional development activity/course is designed for:
- All teachers involved in adult numeracy instruction. Instructors at all levels of math comfort are encouraged to enroll. You do not need to currently teach a math class to fully participate in this course.
Proportional reasoning is the capstone of arithmetic and the cornerstone of all that follows (Lesh, Post, & Behr, 1988). In this course, you will analyze videos of adult students engaged in proportional reasoning activities, deepen your own knowledge of this critical concept through a series of activities, and develop activities and questions for your own classroom that will push your students toward conceptual understanding. The concepts addressed in this course can be found in the College and Career Readiness Standards for Adult Education (CCRSAE) domain Ratios and Proportional Relationships, as well as some of the algebra standards, at levels C and D.
Making Sense of Proportional Reasoning is a blended course composed of two four-hour face-to-face sessions and two week-long online sessions. Each online session takes about four hours to complete. The total completion time is approximately 16 hours.
The course schedule is as follows:
- November 30: Session 1 (face-to-face meeting, Devens)
- November 30–December 6: Session 2 (online, self-paced)
- December 7: Session 3 (face-to-face meeting, Devens)
- December 7–14: Session 4 (online, self-paced)
Participation in the online sessions involves reading assigned materials and participating in online discussions and activities.
To receive a certificate of completion, participants must complete both online sessions and attend both face-to-face-sessions. For more information, please contact Sherry Soares (firstname.lastname@example.org).
Upon completion of this professional development activity/course, you will be able to:
- Identify real-life and mathematical contexts that involve ratios and proportions
- Explain what a ratio is and is not, and whether proportional reasoning is appropriate in a given situation
- Distinguish between different types of mathematical comparisons, and connect multiplicative comparisons to ratios
- Identify the different multiplicative relationships in a proportion, and make sense of them in different contexts
- Use concrete strategies to help students reason about ratios
- Differentiate between activities with open-ended math questions and parallel tasks for adult learners