Reflection Question- Week Two

How did each article help further your understanding for your topic area Mathematical Tools?


Thompson's article, "Concrete Tools and Teaching for Mathematical Understanding" allowed me look further into the importance of concrete tools and what teachers should be asking, "What, in principle, do I want my students to understand?" I also found that concrete materials are used appropriately for two purposes:

• "they enable the teacher and the students to have grounded conversations about something concrete"
• they furnish something on which students can act

From this article, I learned that for concrete materials to be an effective aid to students' thinking and to successful teaching, "the effectiveness is contingent on what one is trying to achieve" and reflects upon the teachers ultimate goal. Meaning, it reflects on whether the teacher is asking, "What do I want my students to understand" rather than "What do I want my students to do". After reading Witherspoon's article, "And the Answer is Symbolic" I was able to grasp a better understanding behind the misconception of what a symbol means in terms of mathematics. I was also able to see the importance of fostering mathematical literacy and the communicative role of mathematical symbols in elementary school.

The use of concrete materials in early childhood education is essential. However, I have learned that it is very easy to misuse concrete materials and to use them incorrectly. As mentioned in the article, using concrete materials doesn't mean that a child will automatically grasp the understanding behind the mathematical meaning of the concrete object. While we must use concrete materials to teach math, it is also important to understand that children must know and understand the meaning and representation of the concrete materials being used.

We cannot assume that each child knows the meanings of symbols and concrete objects but we must make sure that each child understands what the symbols represent in a mathematical expression.

Overall, the articles provided me with a better understanding on the role of concrete materials when teaching mathematics and the importance of fostering symbolic literacy.