Thursday, March 9, 2017

More Meaningful Math Visual Displays...

Allow me to share with you a few more excellent visual displays I have encountered in my recent travels.

Math displays can be tricky.  Sometimes there is too much information, and it gets ignored.  Other times it's great information, but difficult to read or see.

What IS great information to display in math?  How do I make sure my students utilize visual displays for math?

Think about strategies that your students are frequently practicing, and consider constructing a strategy wall for your classroom.  Here are a few nice ones that have caught my eye:

I like this 3rd grade strategy wall (above) because it is designed as a work in progress (note the added strategies below) and it is displayed LOW to the ground, and big enough to read, so it can function as a teaching tool.  It is also on display near a table where small groups assemble to do work with the teacher.  Multiplication fact strategies... so, so important.

Here's another 3rd grade strategy wall that's completely different.  It is displayed high, but it is clear enough to see from student seats and is also at the front of the room, making it easy to refer to as an instructional tool.  Very clear and easy to read. 

Look at all the great stuff on this 4th grade word wall!  It is big and colorful and takes up a whole bulletin board... Who devotes an ENTIRE bulletin board to math?? A GREAT TEACHER, that's who!!  ;^)

This one might be my favorite of all.  Can I make my explanation stronger?  YES!  I love the one star, two star, three star system.  I love the base ten notation included at the top.  This is displayed in a FIRST GRADE classroom.  It's never too early to develop great persuasive writing and mathematical thinking habits.

Here's another one from a first grade classroom.  Number sentences have symbols, numbers, and an answer!  Such a simple, crucial message, and students in this class can't ignore it.  

This is from a sixth grade classroom.  I love the message here, and the white boards placed exclusively for the purpose of posting learning targets.  It makes it a lot easier to get into the habit of posting learning targets when they have their very own white boards.

Here's another display from a 6th grade classroom.  Each component is laminated and kept on file so a unit's essential question can be on display for any period of time, and quickly replaced with ease.  Essential questions are great things to display, since they remind students of the overall mission.  I asked a student in this class to tell me what his class had been working on, and he referred to this display.  "Ratios," he said, "and how they compare and stuff."

Grades 3-5: Talkin' Fraction Immersion Blues

It's springtime in Everyday Math Land, and fractions are all over the place.  In our lessons, we're talking about understanding fractions, comparing fractions, fractions on a number line, area models for multiplying fractions, simplifying fractions, even subtracting and dividing fractions.  And when the topic is fractions, there is SO much to talk about.

Take this problem, for example, from a fifth grade, Unit 5 math box:

I totally love this problem, because there is SO MUCH TO TALK ABOUT here!  There is no doubt in my mind fifth grade students struggled with this one.  For one thing, it falls, right smack dab in the middle of a lesson on multiplying fractions, but... is this a multiplication problem?  Let's have a look at each part.

Gwen is 7/8 of the way through a race.  It is important students recognize that means Gwen is almost finished with her race.  It's an essential piece of information, and it needs to be understood.

Next, we learn that he family was cheering for her when she was 2/3 of the way through the race.  It is important for students to know what that means as well.  At 2/3 of the race, is Gwen almost finished?  Is it as close to the finish as 7/8?

Each of the above two pieces of information could be discussed in a turn-and-talk.  It's likely many students will assume this is a multiplication problem (because of the theme of the lesson), so they need to be given the opportunity to justify that, to prove that the operation is multiplication.  They won't be able to, because it is a subtraction problem.

Through meaningful discourse, students should be able to explore the information given to realize what is being asked.  First we are given one value, 7/8 of the whole (of the race), and then we are given another value, 2/3 of the whole (of the race) and we are asked to identify how much of the whole (of the race) is in the difference (the distance between 2/3 of the race and 7/8 of the race).

So the number model is: 7/8 - 2/3 = X.

The key here is the meaningful conversations, the discourse we want our young friends to experience so we can allow them to form their understanding of the problem.  Encourage debate with problems like these; see if students can justify or prove why they chose the operation they chose.

Fractions are really hard for children to grasp, especially for those who have not become fluent and automatic with multiplication, and/or have not mastered the concept of division.   It is essential they have these conversations to build their conceptual understanding of what fractions are, and what happens when we add them, subtract them, multiply them and divide them.

We need to do what we can to avoid those fraction immersion blues that come in March and April.  It affects students when they are struggling with understanding fractions, and then things just progress too fast.  It seems like one minute they were identifying fractions on a number line, and the next they were dividing mixed numbers.  The fraction immersion blues affects teachers when they find themselves having to explain fractions to frustrated learners a lot, and having to watch their students suffer through the pain of doing math they don't understand for weeks at a time.

Allowing maximum time for students to collaborate and communicate their thinking around fractions is essential this time of year.

Make room for more collaborative work and meaningful math talk by jigsawing journal activities and spot-checking their journal work and math boxes as they work on them.  And let me know if there are ways I can help.