Traveling over the last week and preparing for a wedding really set me back in the schedule so please forgive me! It is summer after all.
The next part of the book focused on subtraction, which can be very difficult for children to understand. The book focuses on similar strategies to piggy back off of addition but the part I really paid attention to was this sentence:
"..how important it is to careful about our use of precise language when teachiing subtraction."
The author discusses an example dealing with negative numbers but I also wanted to make note of a few other misconcpetions that we can create when we aren't careful with our language.
For example, when we subtract and use the word "borrow", I think we are doing our students a disservice. What are we borrowing? Are we giving it back? Where are we placing the numbers we "borrow" and does that follow with the place value strategies we have been constructing with the kids?
Instead I like the words bundle and unbundle. When we do not have enough in the ones place, we unbundle a ten so that ten more ones are created. This may sound nit picky but we have just spent a significant amount of time with our students teaching them to compose numbers in many different ways. Let's say a student is asked to subtract 34 - 7. Instead of "borrowing" a ten, we can unbundle a ten so that we have 2 tens 14 ones - 7 ones. This is easier for the children to see 14-7=7 ones and subtract.
That was my take away from the subtraction section.
How about yourself?
Subtraction is a hard concept for younger ones to grasp- especially when they get to bundle and unbundle (thank you Carrie for those words that I will use with my first graders).
ReplyDeleteSomething I took away from the subtraction section was when it mentioned sharing stories about subtraction. So often we just jump right into the teaching of something that we don't try to relate it to the students or let them relate to it themselves. I think I want to spend some time on them sharing stories where they subtracted and charting them on paper so they can make the real life association. If they can't come up with any at first, I would share a story of my own to get them thinking. I might even do this in groups and let them talk with each other about times they have subtracted. I bet they would love that!
Something I thought the children might struggle with (ok struggle more with) would be during number bonds when you want them to work systematically so they don't miss any combinations. This will take a lot of modeling and practice to get them to work in a sort of order rather than just coming up with any number bond. (In case you are unsure of what I am referring to- 11-10=1, 11-9=2, 11-8=3 (in number bonds)).
Also, something else I found important to focus on was during place value disks. After you build the number in the tens and ones columns, you take away what you need to. Students need to be asked why you don't need to build the second number (because you are taking something apart). Sometimes they forget and build both numbers and need to think about what they are supposed to be doing in the problem.
Do we have place value disks at school? I don't think I've ever worked with them before.
Place value disks can be ,ade using those two-sided yellow and red disks or even poker chips.
DeleteI really love the idea you mentioned regarding the student talk. I think that all students have a story they can tell about losing or giving something away. By having them talk about it, you are involving all students, even those who may be struggling students. Everyone has a math story!
ReplyDeleteI agree. Word choice is not nit picky, but necessary. Precise language leaves less room for confusion. Many students are not sure why you would be able to borrow from one number and not be able to borrow from another.
I look forward to using the Singapore math subtraction strategies with my students even in fifth grade. Subtracting across zeros was always a skill I had to re-teach. The kids were more focused on "crossing out" and adding a "tick mark" than really comprehending what was actually happening to the numbers and their place values. My hope is that this concrete representation will stick solidly in their minds and connect to the process of subtracting the algorithm. If kids get stuck on a problem, hopefully they will be able use the picture representation (t-chart and disk drawing) to figure out what to do and problem solve through the algorithm.