This week’s readings examined using tools for learning, and developing fraction concepts. The readings were a good reminder than having tools such as manipulatives and technology available does not ensure that learning will occur (103). The mathematics connections may seem obvious, but that is because the teacher already knows the math. For students, though, the math connections are not obvious. That is why is it important for teachers to help students make the connections (105) . . . without stifling mathematical thinking and creativity.
In this way, tools are a lot like rich tasks. The most creative rich task is a flop if the teacher does not plan with mathematical connections in mind, and then fails to allocate time to ensure students make the intended connections between strategies (or in this case, tools) and the mathematics. (55). Having cool tools such as manipulatives and technology is great, but just because students use them does not ensure that learning will occur (103). Teachers need to ensure that the tools enhance the lesson, and do not become the primary focus of the lesson.
Using tools has its perks, such as when learning fractions. The text says that students struggle with fractions but evidence shows that effective use of models in fraction tasks is important (286). The text offered several suggestions, such as paper folding, filling in regions with fraction pieces, and counters in two colours. The use of physical tools allows for stronger connections to mental models, which enriches students’ understanding of fractions (286). The tools take a symbolic idea and makes it concrete (286). Without these physical tools, students may not make the leap to mental connections. I also think that physical tools, such as blocks and bead chains, help kinesthetic and visual learners understand because they are mobile and hands-on.
The text suggests giving students free time to play with manipulatives before beginning the learning activity. I laughed when I read this. Students may see base ten blocks fun stacking toys instead of tools to teach place value (105), but it is up to the teacher to reinforce that these are tools, not toys. I can only imagine the chaos that would occur if the teacher gave students time to get their meter stick sword battles out of the way before getting on task, so why allow playtime for smaller tools? If students want to use base ten blocks as stacking toys, allow it during dedicated play time, such as indoor recess. During math time, though, the manipulatives are learning tools, not toys.