Week 2, Challenge 5

"Kindergarten is More Than Counting" is about helping students become fluent with numbers. As long as students have manipulatives, they are more likely to count by ones to reach an answer. The author suggests using a Quick Image format to help students learn patterns and number characteristics. By flashing images of dominoes for fewer than 3 seconds, students learn to rely on pattern recognition because they do not have enough time to count the individual dots. After doing this, the author suggests using story problems. She says that students need to learn patterns and the qualities of numbers before they can learn how to take numbers apart and put them together, the ultimate sign of fluency.

"Understanding Children's Reasoning" states that the most effective way to understand a child's thinking is to ask them to explain how they reached an answer. The author says that the teacher must always be analyzing comprehension by asking questions such as, "How did you get that?", "Why did you start there?", and "How did you know to ____?"

"Thinking Strategies: Teaching Arithmetic Through Problem Solving" says to begin by learning the students' different conceptual levels, such as using fingers, using manipulatives, working with number lines, using pencil and paper to draw, using pencil and paper to write, or creating their own way. To teach thinking, this author also suggests using Quick Images to help students recognize patterns and learn step-by-step thinking. The author recommends using a balance (tangible or hypothetical) to practice balancing problems as well as relating known problems to new problems. She says it is always beneficial to see what the students can come up with on their own first and work with that because children should be given more responsibility in the learning process in order to retain information.