One of the concerns that teachers have mentioned is that they worry that students won't use manipulatives properly, or they might not stay on task at a learning station. There is definitely the need to spend time building an understanding of manipulatives as tools rather than toys. There are a few different ways you might achieve this in the classroom.
Strategy 1: Explore together.
The first time you expose students to a particular tool, take some time as a class to explore this tool with a mathematical eye. Imagine putting the tool out for students to explore independently but alongside others who are exploring, too. After a few minutes, have students turn and talk, or get into small groups to talk about how they see the tool helping them with math. As a large group, discuss and brainstorm some of the uses of the tool.
SAMPLE ACTIVITY - Grade 2+ Geoboards
Give students the opportunity to look at the geoboard without an elastic. Ask them to look for as much information as they can on the geoboard (number of pegs, number of squares, size, layout, etc) There is a great article by Marilyn Burns about the first time she introduced geoboards to students at the link below. In fact, it's a link to a publication called "Hands on help from Marilyn Burns". For interest's sake, note that the publication date is 1996!
Once the students have had some time to explore the geoboard and notice the details, have a large group discussion about their findings. Then, ask them to look at their findings and think about how they could use this as a math tool. A few years ago, I had the opportunity to do this exploration with over 90 classrooms. The thing that blew my mind was that in each case (in classrooms from Grades 2 to 6), students came up with great ways to use the geoboard that related to all 5 strands of math. Often, their teachers were totally surprised at the ideas they came up with. Usually, we used their thinking as a springboard to come up with a follow-up lesson. You'll see an example of such an activity, below.
Strategy 2: Provide students with an open prompt that will encourage them to use a manipulative to represent or to support their thinking.
SAMPLE ACTIVITY - Grade 1 - Cuisenaire Rods
One of my colleagues introduced cuisenaire rods to her students with an exploration activity. During their exploration, they noticed that the rods could be organized by length, and that there was a relationship in their lengths (each one is 1 cm longer than the other). Because of this exploration, the students were able to assign values from 1 to 10 to the rods. The students were looking at number bonds, and they began to use cuisenaire rods to find all of the possible ways to make 7, for example. Not only were they able to model the 7s using the rods, but they were also able to represent their rods as numerical expressions, and to engage in rich discussion as one combination led to another.
SAMPLE ACTIVITY - Grade 3/4 - Geoboards
As students begin to formalize their understanding of fractions, it can be helpful for them to see that a geoboard can be divided into 2 halves, and that the two halves may not look alike, but each half will have the same area. One way to explore this concept is to ask students to show one half on the geoboard. Students can record the different ways to show one half either on dot paper, or by taking photos of their geoboard and posting it on an electronic bulletin board, or by using a single device to photograph their work. There's a great geoboard app (it's free!) that can also be really handy for this, as students can screen shot their work and then compile a slideshow of examples, or find another way to compare their different solutions.
I've been reading through the "baggage" (barriers) that participants identified heading into our workshop sessions last weekend and noticed some interesting similarities, and some topics that haven't come up in previous sessions. I thought maybe I would try to respond directly to some of the "baggage" in my upcoming posts, so that maybe some of the baggage can just be left behind. I'm also hoping to add samples of math stations as they evolve in my classroom, which might help others.
Here are the slides and the participant work from the Math Learning Stations workshop. I've added the participant contributions (the learning stations that groups created) directly into the presentation from session 2. Thanks so much for sharing your ideas with everyone. I appreciate your willingness to participate and to take a risk or two.
It was a beautiful day in Sault Ste Marie and a pleasure to work with teachers and administrators, thinking about technology and math and learning stations. Here are the slides from both sessions. I've added the participant contributions (the learning stations that groups created) into the presentation from session 2. If you have any questions or comments, please contact me using the contact tab above. Thanks!
As the President of NOMA (the Northern Ontario Mathematics Association, I'm really pleased to be in Sault Ste Marie this weekend to present a couple of workshops at the NOMA Spring Mini-Conference. Traveling here with my colleagues from Sudbury was lots of fun, and now I'm just putting the final touches on my presentations for tomorrow morning. I'm looking forward to talking about Using iPads to gather evidence of student learning, and to model and develop learning stations for the math classroom. It's always a pleasure to work with other teachers, and to take the time to pay attention to mathematics.