What is Guided Math? WE SAT DOWN WITH OUR LOWER SCHOOL MATH SPECIALIST, J E N N I F E R H O G A N (who also writes a popular
monthly math blog for Scholastic) to get the lowdown on how Guided Math prepares students to go beyond “learning math” and start thinking like mathematicians.
Q: What is Guided Math, and why is this approach beneficial for our students?
A: Guided Math is a contrasting approach to whole group teaching. Traditionally in math, the teacher would stand at the front of the class and everyone would sit at their desk learning one specific concept. The idea being, “Okay. Everybody do it like I’m doing it up here at the board.” Unfortunately, that’s why people got the notion that you were either good at math or you were bad at math because students could either follow the directions or they couldn’t. Guided Math is a way to teach in small groups so that the teaching is more individualized and targeted for each learner. Math is so fluid. A student could be really good at multiplication but struggle with subtraction. One of the key components to Guided Math is the idea of pre-testing. By pre-testing every unit we see where our students are, and can target the lessons so students move forward at their own appropriate stages.
Q: Can you give a specific example of what this process might look like?
A: Let’s say in third grade, I’m introducing multiplication. I have a small group, leveled for multiplication. Another group would be working on regrouping with addition or subtraction, a concept we’ve already learned, but need to continually practice. The third group might be engaged in a technology game, like reflex math, or they can be doing another fun math activity. Everything is about student engagement. The groups only last between 12 to 15 minutes. Then they get up and move to another group instead
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of waiting until everybody is done with a particular workbook
We want students to really internalize the learning and be able
or problem. Students are constantly engaged, and we find that
to transfer that to different scenarios. The ability to go back and
they’re really building on concepts in a more concrete way. So
forth, to be flexible learners, is really imperative to reach a deeper
that’s what Guided Math physically looks like.
understanding of subject matter.
Q: How does Guided Math affect the way students
Q: That’s not just math-based, but pertinent to any type
are assessed?
of learning, isn’t it?
A: Every day we have one or two objectives and when the
A: Right. It crosses over. I talk about math as if it’s a language,
lesson is over, you know whether the students have achieved
and I compare it to how students learn their A-B-Cs—every
that objective or not so you can then form your ongoing
letter has a sound, and when you put those sounds together, they
approach. This is formative assessment. It’s ongoing. If everyone
create different words with different meanings.
were working on the same thing at the same time—you can’t troubleshoot on the fly. You have to wait. So, this is a proactive approach to teaching, instead of reactive.
Well, the same thing happens with numbers. There are only 10 digits. As long as you know those 10 digits, you can put any numbers together and make different numbers just like different
I’ve heard teachers say how much better they feel about what
words. You need to be able to speak this math language. It’s not
their students know by the end of each lesson. They feel
just about, “What’s the answer?” It’s about, “How did we get
like they’re getting to know each of their students, and their
there? What does it look like? How do we talk about it? If I
strengths and weaknesses, within one lesson.
change this, what does it look like now?” Just like reading. You are going to build on those concepts every day, every year, or
Q: How do you think this changes the students’ perspective of math?
A: It’s more engaging for Lower School students to be moving, and not sitting so much. They don’t even realize how much they’re learning, and how much practice they’re getting, when they’re playing the math games. And they are having so much fun. They are more confident; they’re enjoying it more… and that gap of “good versus bad” math students really closes.
every chapter. It’s about developing number sense.
Q: Could you define number sense? A:
Sure. [chuckle] This is always a tricky one.
It really has to do with the ability to look at numbers in different ways. Being able to pull numbers apart and put them back together. In Kindergarten, for example, a child has a strong number sense if they can look at the number 10 and decompose
The students are talking about their math now. They’re not just
it and break it apart in lots of different ways. Instead of just
doing it. They are exploring concepts on their own, and they’re
telling me that 6 + 4=10.
coming up with unique approaches. I have three questions that I pose in my classroom, and they are written on the board. One is, “Why?” The other one is, “How come?” And the third one is, “Can you find another way?” It’s about open learning. An open question in math would be “What are some different ways to make 10?” versus “What is six plus four? What’s five plus five?”
Q: Do you see more of their natural curiosity in math
A child in third grade can look at a fraction and see where it’s placed on a number line. They can talk about other fractions in comparison to it. They can say what’s an equivalent fraction, without doing that through any type of algorithm. They’re just looking at the number—the fraction itself—and saying, “Okay, well I know that 3/8 is less than a half, and I know that something like 3/4 is greater than a half, so 3/4 has to be greater
subjects using this kind of approach?
that 3/8.”
A: Absolutely. We’re really creating problem-solvers who are
We’re even starting to teach algebra in first grade with the idea
able to attack different questions in different ways. We want
of using the number balances, so that a first grader can tell me
them to really persevere with the problems.
that 3 + 1 is the same thing as 2 + 2. They are able to look at an
One of the most important skills around math is flexibility. When
4. But if you don’t understand what that equal sign means or you
I see a flexible math thinker, I know they’ve really mastered a
don’t have a concept of the number 4, you’re just going to say
skill. If students learn math through rote memorization, then
no, “It looks different and it looks funny.” By using a tool like
as soon as something looks different, they’re not flexible. They
the number balance, they realize the equation is balanced. It’s all
can’t transfer it. They really haven’t understood it or mastered it.
about getting them to really have more of an open mind and not
They’ve only figured out how to solve the problem one way.
be so rigid in their math thinking.
equation that 3 + 1 = 2 + 2. And they understand that because 4 =
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