Has this ever been you?
Um, yes. Me too. There are so many times when I want to get inside a student's head to figure out exactly what he/she is thinking.
It's GOOD for students to explain their thinking. It helps solidify their ideas and their learning, as well as help them clear up misconceptions on their own.
In order to develop our students' verbal reasoning, I looked for a way to frame their thinking and become independent in their explanations.
I started looking in to Visible Thinking - and I love it!
Visible Thinking has routines that help students frame their ideas and discuss their thinking. These can be done verbally, in writing, or both!
In 5th grade, we started comparing decimals with a class discussion. Students had to compare 2.587 and 2.98. Of course, they picked 2.587 as the greatest, because 2.587 was longer. This started a great discussion about the value of each digit. At the end of the class period, we wanted to see how students' thinking had changed through the discussion. We used the routine "I used to think___ but now I think____". Students completed this on their whiteboard, and it was very interesting to see what they came up with.
In 4th grade, we used the "See, Think, Wonder" routine to explore rounding numbers to different places. I wrote on the board a series of numbers, such as:
527 --> 530
642 --> 640
987 --> 990
Students first discussed what they saw. This is simply surface-level observations. Then, they discussed what they thought about what they saw. This gets a little deeper into what is happening with these numbers, what the pattern is, or what the "math" behind the numbers is. Then they discussed what they wondered, which gave me a good gauge as to what they knew about rounding and what gaps they had. Students first thought about their response, then discussed with a partner, and then shared with the class. This kept all students engaged in the routine.
I love using the Visible Thinking routines because it's like opening up a student's brain and seeing what is going on inside. These routines also develop ELL's language in math, especially at the discourse level. It also helps students have a clearer understanding of their own thinking.
Check it out for yourself, and leave your experience in the comments!
In my opening for math workshop I try to incorporate some kind of number sense warm up... and my students have fallen in love with SUBITIZING!
Have you done your subitizing today?
Subitizing is the ability to recognize a number WITHOUT having to count the quantity one-by-one. Yes, initially students need to learn how to count one-by-one, but don't spend too much time focusing on counting! You want students to see quantities as a SET. When students establish this skill it allows for them to visualize and hold quantities in their mind. When students can hold amounts and visualize quantities in their mind, they are then able to decompose and manipulate the numbers - building greater number sense - BINGO!
The best way to start this in the primary grades is to encourage the use of a NUMBER PATH (from Mathematically Minded). Why a NUMBER PATH you ask? Check out this great comparison of Number Paths vs. Number Lines HERE!
A favorite number path of mine would be this version which I love for introducing and finding patterns in multiplication - amidst many other uses!
Ok... back to the warm-up!
Many resources will work to get you started and your students thinking!
Create a variety of flashcards with pictures of:
10's Frames (from Oceans of First Grade Fun)
Rekenreks Set1 Set 2
(or make your own using index cards or paper plates with stickers)
General rule is to start slow with visual quantities of less then 5 - flash any visual representation & remove.
Ask students what number they saw and how they came up with that answer. Once quantities of 5 are established, you can move onto quantities of 6-10, and then onto quantities of more than 10.
Here's some additional cards to print out and use as quick warm ups
or when you have an extra 5 minutes!
Make the time! Students' number sense depends on this!
P.S. It's never too early to start! Meet 5 year old Elyse. She loves doing dot patterns with her grapes...
... well, most of the time :)
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