Think About It!: The Next Installment

It's been a while since the last post! This has been the busiest month ever!!

Anywho, I finally decided upon the next installment in the series. I can't tell you an exact posting date right now, but I am pretty sure it will be in February! :)

The installment will include ideas for using manipulatives and, more importantly, why you should use manipulatives. I'm also thinking this will turn into a linky party (how fun!). Stay tuned for more details! :)

Think About It: Tricks for Learning

Only a day later than promised...

Okay, let's hear 'em! You still remember a trick (saying, phrase, chant) or two that helped you memorize something from your own school days! My favorite one for math would have to be for the quadratic formula. My high school Algebra 2 teacher taught us to memorize it by singing it to the tune of "Pop Goes the Weasel." I will do my best to describe to you how it goes since you can't hear me singing it! I put the lyrics of the equation song right underneath the original lyrics so you can put the tune to it.

Here is the actual formula:

And here is the song:

All around the mulberry bush,

x is equal to negative b

The monkey chased the weasel

plus or minus the square root

The monkey thought 'twas all in fun,

of b squared minus 4ac

Pop! goes the weasel.

ALL over 2a!

Were you able to figure it out??

Teachers (myself included) are notorious for coming up with (or googling) little tricks such as the one just described to help our students along the way: songs to help memorize formulas, clue words to use during problem solving, and phrases or chants to help remember procedures (to name a few). My kids love to learn a new song or rhyme, especially when there are body motions involved!

Ever been frustrated when teaching because you know you taught them how to memorize something and it was the coolest little trick and it's so easy and they just. didn't. get. it. ??

Let me give you an example:

My kids are responsible for understanding the difference between area and perimeter and applying that knowledge to problem situations. I find that, most often, they were taught "to find perimeter, add all the sides" and "area equals length times width." Some of them even knew a cute little song to go along with it. The kids can spit back the formulas all day but when it comes to application they struggle. They want to add length and width when finding area and multiply when finding perimeter. I used to ask, "WHY don't you get it?? You can tell me how to do it but you aren't doing it!" OR "The poster is right there--why aren't you using it??"

This all boils down to two major questions: Do your students know what they're memorizing? Do they understand the process of that which they are describing in the songs and rhymes?

I think those questions are very important. If the answer is NO, then there is a problem. Songs and such must connect to actual concepts and learning if they are to benefit students. Just learning a song is not the answer. Students still need to have an understanding or perimeter and area instead of just learning a song that describes the difference between the two. If there is no connection to actual learning then learning such songs is fruitless.

On the memorization side of it, the kids are more likely to get involved and retain it if the rule, trick, or song process involves them. They will naturally take ownership if they (not just the teacher) came up with it. (Of course you know that kids (and people in general) are naturally more interested in things that pertain to them or things that involve them.)

Along with that, people learn best from self-discovery and hands-on experiences rather than direct instruction. That is why so many of us use hands-on inquiries and anchor charts in our classrooms. Think about it--how many kids learn that the stove top is hot not because mom and dad keep telling them so but because they touched it??! I think self-discovery is especially important when coming up with clue words for problem solving. We want to be able to help our students work through problems by giving them words to look for (especially with all of this stupid standardized testing going on). Allow students to find the words on their own (scaffold, if you will). Telling them "each means divide" and "difference means subtract" makes them think that it is true every time, no matter what context, which is VERY hard to break (all of my students came in thinking that each means to divide every stinkin' time, no matter what!). They will better understand if they are able to see the operation in several different instances. Here is an example of an anchor chart that my kids came up with for multiplication and division:

My kids want to use the anchor charts because they helped make it.

My point is this--involve your students in coming up with these "tricks" as much as you can! I am not against these activities as I use them in MY OWN classroom. I just want to emphasize 1) that we shouldn't rely solely on the songs and rhymes to teach for us, 2) it has to be meaningful if we want it to stick and 3) self-discovery is important.

Here are just three of MANY things you can do:

• Give your students the challenge of coming up with their own songs to assist in learning. (I've read about lots of you in bloggy land already doing this!) 
• Create anchor charts with your students. Students are more likely to retain the information if they are a part of documenting it. (I got rid of all of my store-bought posters and have replaced them with anchor charts that we have made together.)
• Let your students learn by self-discovery. Instead of telling students, "equivalent fractions form a pattern when lined up side-by-side," guide them in seeing it. Have them line it up and ask, "What do you notice??"

Well...that's all I have. A day late and posted way late in the evening... :)

THANKS FOR TUNING IN! I would love to hear your thoughts!! :)

*I received a few emails from you about being willing to post a list of your math music that you use. I'm thinking either linky party or separate posting (depending on how many people are to contribute). Anyone else out there willing to share what music you use? Comment or shoot me an email!

Think About It!: The Next Installment

I am SO excited about the wonderful feedback left in regard to the "Think About It!" series! You all have totally embraced it which makes me that much more excited about posting! Thanks to all of you who have read it, whether you commented or not. I think you can tell how strongly I feel about the subject so I appreciate you taking the time to read and reflect.

I am happy to announce the next installment topic:

This is in regard to using songs, phrases, clue words, etc. in teaching kids mathematics. You can look for the post either Monday night or Tuesday night--not sure which day yet!

Also, I have been contemplating having some of YOU join in and guest post an installment of the series (at some point). Would anyone be interested in doing that?? Comment or email me if you are! :D

Think About It!: The Equals Sign

Ask yourself and answer these three questions:

• What do you understand the equals sign to represent?
• What do you teach your students about the equals sign?
• What do your students understand about what the equals sign represents?

8 + 3 = 11

12 - 5 = 7

33 x 10 = 330

Most people understand the equals sign to show where to put an answer. When they look at the above number sentences they will likely interpret the left-hand side as the problem and the right-hand side as the answer.

A few weeks ago, I started having my classes work on basic number sense (since they still don't have it in 4th grade--a future "Think About It! discussion!). The very first thing we talked about was the equals sign. I asked them what they knew about it and all of them told me something along the lines of "it means the answer" or "it means 'is'; where you put the answer." I was a little taken aback and suddenly realized why they struggle with very basic problems such as 12 + __ = 20 or 7 x __ = 140. (Do your students struggle with those too?)

I have seen several recent studies that involve asking students the same questions about the equals sign. Let's, for instance, use 4 + 7 = __ + 2. On problems like these students would oftentimes add 4 and 7 and place the sum in the blank so it reads 4 + 7 = 11 + 2, completely ignoring the 2. I'm sure you as an adult (and teacher) look at that and instantly understand how the number sentence and thinking is wrong. Unfortunately, most students will not.

The equals sign indicates equality. It is placed between two things of equal value. Think of it as a balance. So when you say 8 + 3 = 11, you are saying that 8 + 3 has the same value as 11.

Can you see how knowing this in elementary school will help students better understand algebraic equations?? When students are learning about evaluating algebraic equations such as 3x + 7 = 28 they MUST understand that both sides are equal or they will never understand how to solve for x. The time to teach this is NOT in middle school but in the early grades.  

Students should also understand that one side of the equal sign does not always have to have a single number. The equals sign can show two expressions that have the same value, like 9 x 4 = 12 x 3.

I want to address one more misconception--the running equals sign. Here is a word problem and example:

Sally had 4 marbles. She cleaned her room and found 3 more marbles. Her friend then gave her 8 marbles. How many marbles does Sally have now?

Number sentence: 4 + 3 = 7 + 8 = 15

How is that wrong? Remember, both sides have to be equal. The correct way to write it would either include multiple number sentences or parentheses:

(4 + 3) + 8 = 15

OR

4 + 3 = 7

7 + 8 = 15

I wouldn't say repairing this misconception is a quick fix, but it is definitely doable. (And, of course, it would be better if instruction about the equals sign is correct from the beginning.)

• You can start by having a discussion about it with your kiddos. Bring in a balance to help you explain (for instance, put two pennies on one side, then add 6 more to it. Record that as 2 + 6. Then add pennies to the other side (8) and let your students witness how the trays become balanced. Record it as 2 + 6 = 8.)
• Another activity would be to have students use equality cards. You can make some simply by putting a number sentence with one missing number on one card and have the students match it to a number sentence in the same fact family with a different number missing (e.g., 6 + __ = 8 on one card and 8 = __ + 2 on the other.) Look for a free Equality Card activity in my Teachers Notebook store!
• You could also make a mat with an equals sign and have students place cards of equal value on either side of the symbol. The cards could contain pictorial models, standard form, expanded form, etc.

Sidenote: I'm not sure if you are familiar with the National Library of Virtual Manipulatives--if you aren't, you NEED to be! It is exactly what it states. The site has every manipulative imaginable in virtual form for FREE. It also has activities to go along with each.

To those that teach the higher grades--check out this balance that provides visual representation of algebraic equations:

Awesome, right?!?

Even if you don't teach the higher grades I encourage you to check out the algebraic equation scale and ponder about how easy it would be for our current students who do not understand an equals sign.

Think about it...

I always enjoy incorporating literature into math class. I have not actually read this book but it looks like a cute little story about creating equal sides. Check it out by clicking on the picture.

Thanks for tuning in. I WOULD LOVE TO HEAR YOUR THOUGHTS! THROW 'EM AT ME! :D

Also, I would LOVE to tell you to look for these posts on a certain day and time but I can't right now--life is not that predictable! Installment number 2 will be before school starts back though! :)

New Series: Think About It!

I am excited to announce that I am starting a new blog series entitled "Think About It!" The purpose of this series is to encourage you to think about/reflect upon how you are teaching math. I have learned so much about teaching math this past year (mostly due to working on a masters in math curriculum and instruction). I want to challenge you in the same way I have been challenged. The first post will be:

Expect to catch part 1 either tonight or tomorrow--thanks for tuning in! I hope you are as excited as I am!