Have students explain their model to their group, particularly how each method means the same but might be more appropriate in certain situations. This can be done in small, medium and large groups, and also allows students to improve communication skills. 6. On a given worksheet, allow students to peer assess their performance, then meet and discuss the results and ways to improve. By reviewing other student's performance, sometimes the individual weaknesses one student may have are mitigated. This changes the way students often approach a problem, as well as engendering empathy skills.

7. Think-Pair- Share -- at the think stage, instructor asks a question and asks students to think about it for a few minutes, writing notes, etc. If needed. Then students pair up to discuss their approach to the problem; finally, students share with the class in a communications interaction activity. The sharing and pairing often provide differing points-of-view for the lesson.

8. Use blocks or other manipulatives; ask students to visually represent a group of ratios using the manipulatives (Kinesthetic learning). Alternatively, students could visually represent the process. Using manipulatives also offers an alternative explanation of how ratios or other mathematical processes work.

9. Make four broad statements about ratios (formation, use, etc.). Post these one at a time; have students...

If time, have students explain their reasons to each other, another group, or the class. Switch questions to find out ways students are processing the information.
10. When ratio lesson is over, have students take a few moments to reflect in their learning journal -- what was new, what was useful, what was not, and why it might be later? Also, how can the concept of ratios be used in real life? This journal is kept by many mathematical or scientific professionals and can be used as a reference as students learn to master increasingly difficult concepts.

REFERENCES CONSULTED

Fisher, D. et.al.. (2007). Checking for Understanding. Alexandria, VA: ASCD Press.

Hall, K. And Burke, W. (2004). Making Formative Assessment Work. New York: Open University Press.

Keeley, P. And Tobey, C. (2011). Mathematics Formative Assessments; 75 Practical

Strategies for Linking Assessment, Instruction and Learning. New York:

Corwin Press.

Kim, S. (2005). The Effects of a Constructivist Teaching Approach. Asia Pacific

Educational Review, 6(1), 7-19.

Tobey, C. (2010). Uncovering Student Thinking in Mathematics: Formative

Assessment Probes for the Elementary Classroom. New York: Corwin

Press.