Mental Math
This was our first week of class learning about the fundamentals of elementary math. In class we were assigned a few different subtraction problems to solve in our head. I am not too fond of math on a personal level but I figured this couldn't be too hard. After a few minutes we talked with our table group about the way we solved the problem and then were assigned to form groups with other students who solved the problem the same way. I used the traditional regrouping way to solve the first problem. The problem with this method is that we were taught in school that you can't take 9 away from 6 so you must make the 6 a bigger number. The problem with that statement is that later in math kids will learn negative numbers and have to do 6-9 but won't understand how that is possible. Christina used a really good example in class that kids may not understand the actual term "negative number", but they can understand the concept of owing somebody $3.00. It's really important that we as aspiring teachers learn to the right WORDS to say so that our phrases don't impact the kids idea of math in the future when they discover that you really can have negative numbers.
66-29 = 37
I lined the numbers up like we were taught in 2nd grade and crossed out the first 6 to make it a 5 and so on. I ended up getting the answer 37 which was correct. The problem with this method is dealing with 66 as two separate numbers instead of thinking of it as a whole count of 66 crayons for example. It was really interesting to see the other ways that people in the class solved the same problem. Some people changed the 29 to a 30 to make a friendly number. I had never heard that term "friendly number" before. The tens numbers are referred to as "friendly numbers" because it is easier to add or subtract from a number like 30 as opposed to 29.
After we went through all of the mental subtraction problems, it was brought to our attention that you never have to actually subtract. When Christina first said this I was pretty confused but curious to what she meant by that statement. Instead of understanding the actual concept of subtracting, like many kids, I would just go through the motions of regrouping hoping to get the correct answer. Most people are better at addition than they are at subtraction. With the use of a number line you can actually add to find the correct answer and it makes the problem much more visual for kids to see how you got the answer you got.
Using the same example of 66-29 = 37 here is the number line method of finding the same answer using addition rather than subtraction.
1. You can add one to get to 30 which is a friendly number
2. from 30 it is fairly simple to go to 60 so you can then add another 30 (still dealing with friendly numbers)
3. from 60 it is easy to count up 6 more to get a total of 66
4. using proportional arks is important to show the space between numbers on the number line so the child can easily look at each ark to add up 1+30+6 = 37
This blog very specifically explains exactly what was gone over in class throughout the week. I really like how your explanations and pictures explain the positives and/or negatives of the way the problem is being solved and how it related to the learning processes of kids. I like how you explain in detail how one way of solving a problem can specifically be challenging to a younger student and then explain how the other method is easier for them to understand and how that method helps avoid confusion. Very thorough and well organized explanations!
ReplyDeleteI really loved reading your blog! You went through every single step one by one to show exactly how you solved the problem and how a kid might see the problem and solve it in their own way. Your pictures were very helpful and creative! I also liked how you showed the final product using the number line that our teacher used in class. That was a much easier way to solve it and made a lot more sense!
ReplyDeleteI really enjoy how you did this blog, you went into great detail about everything we did in class, little things I did not even remember, you have in your blog. So that was very good refresher information. I like how you explained what you did, but I also feel like there should be a little more compare and contrast. There is plenty explanation but not enough on how things are harder or easier. I love that you put in the time-line method because that is one of my favorite ways that she has shown us so far. It really lets the kids visualize and see what they are doing.
ReplyDelete-Amazing blog site and post by the way! :)
Your blog immediately caught my attention and made me want to continue reading more! Usually when I see multiple paragraphs I usually get bored and just skim through the context. Instead I wanted to finish reading each paragraph and get to the next segment. The pictures were helpful, and brought your words to life! I am a visual learner and often need a picture or diagram to follow the text. It was nice how you compared your thinking process to other peers, and children. Because not everyone thinks the same way, yet they can all receive the right answer. Also, I liked how you mentioned a key point made in class this week. That using the right words are vital in a classroom. Your blog was definitely refreshing!
ReplyDeleteYour blog is pleasant to look at and easy to read. I can relate to you on being a visual, hands on person. I like how you drew a picture of a timeline to get the subtraction problem. I used the stack and borrow method and its hard to do that in your head. But the timeline is easier to picture in your head especially being able to break down into smaller chunks.
ReplyDeleteYour blog is very organized and neat. Your first paragraph is very detailed as to what we did in class in the first week. I love how you included a picture of what you did to solve 66-29 with the stacking, also because this was my strategy! As you went into other strategies, those were also very descriptive with pictures and good explanations. Adding the number line strategy was a good choice because that was an important part of what we learned!
ReplyDelete