Khan Academy Idaho | Shelby Harris & Kuna, ID

This is the teacher I mentioned in my previous post. Thoughts?

Fractions are FUN...

...and teaching them is even more fun! Teaching them so students truly understand can also be quite difficult, so it is important that we as teachers approach this topic carefully. I learned today how much of an impact language can have on student understanding of math concepts.

I have often used the words "out of" to explain fractions: 1/4 is one out of four, 3/8 is three out of eight, 6/10 is six out of ten. This leaves students thinking that 1/4 is greater than 3/4 because 1/4 has just one piece taken out of it (leaving 3 pieces), while 3/4 has three pieces taken out of it (leaving one piece). You "take more out" with 3/4, so it most be smaller, students reason. The teachers language leaves them with the opposite answer. Fancy that! I never would have realized this on my own - what an awesome opportunity to get into the minds of my future students. Understanding a student's thought processes when making an error is the first step toward helping him or her correct that error.

As a substitute teacher, I have helped several students with problems involving fractions. Just last week, a student told me to talk in "kid language" while explaining fractions. This was humbling, as I felt I was using very clear, easy-to-understand terms. Looking back on this experience, I realize I used "out of" in my explanation. Oops.

I was trying to explain how mixed numbers and improper fractions can be used interchangeably. This student was puzzled by mixed numbers. We worked with 1 1/4. He pointed to the first 1 and then the second, very confused. "How can we have more than a whole? We have one already." I made some silly putty pies to demonstrate. By the end of our conversation, he recognized we had one whole pie and that the 1/4 was part of a second pie. This was definitely an "a-ha!" moment.

Next, I partitioned the first pie into four pieces (imagine in my graphic - I'm new to Canva and am still struggling some, though it's awesome), so we could count five total pieces to get to the improper fraction 5/4. I didn't get too far on this explanation. I could tell the student was drained from all of the hard thinking we had done. Plus, I had been so totally "in the zone" talking to this student that I had neglected the numerous raised hands and "Miss Harrison's" throughout the rest of the classroom. I decided to call it a day and went to answer the other student questions. I faced a teacher's dilemma that day: I could either focus on truly and fully explaining concepts to this one student who was struggling so, or I could brush the topic's surface while assuring everyone in the class got his or her questions at least partially answered.

Khan Academy has some amazing videos explaining fractions in a straightforward, easy-to-understand way. In the documentary Teach, a math teacher implements a model of blended learning in which students work on Khan Academy on individual computers. I think this is an awesome way for students to work at their own pace and develop a solid understanding of topics before moving on. It would, however, be hard as a teacher to relinquish this "control," as this model isn't generally what we picture when we think of teaching. As great as this program seems, I would still be sure to pull struggling students aside in order to enhance their understanding with manipulatives, especially for a fundamental topic like fractions.

I am happy my struggling student understood at least a fraction (punny, I know) of what he needed to know the other day, but I am frustrated that I couldn't help him more. Has anyone else been in this boat? Please share!

The sea of zeros...adding and subtracting integers with colored counters!

Adding and subtracting integers with counters is such a fantastic idea. The woman in this video uses little pieces of paper as counters, which works also. She puts numerous positive-negative counter pairs together to create a "Sea of Zeros" that students can access when doing integer addition and subtraction.

This blogger places the "Sea of Zeros" on an organized "work mat" template for students. The work mat also includes 1) a place for positive and negative counters not in zero pairs and 2) a number line. Students can see clearly that the result is the same whether obtained through number line or integer counters. I really like the organized format:

Unfortunately, I haven't had the opportunity to watch this method in action while subbing. I've gotten to teach equivalent fractions (multiple times), so hopefully this will be covered in future chapters so I can discuss this some.

Subbing has been challenging. Fortunately, I was able to sub in the same second grade class for four days. It was so helpful getting to know the students. It's near to impossible to run a classroom without knowing student names. On the first day, I used a lot of "Hey buddy," and "Dear, can you ____." The third day was the best. I used a "magic wand" to give out points for attentiveness, kindness, respect, etc. and take away points for talking out of turn, being off talk, disrespect, etc. Whole class points were available, as well, for outstanding behavior. These were exciting to give.

I subbed in Kindergarten again, although I had previously decided Kindergarten wasn't for me. This experience was better but wasn't without its share of challenges. Math time consisted of counting songs 1-100 and numbers in the teens. Love the energy these little guys produce.

That's all for now! Keep those hearts and minds a'bloomin'!

-Miss Elizabeth