Monthly Archives: July 2013

How do we build on what students can do?

I spent the last week at a lake house with my family.  It was great to be away from the craziness that is New York City.   It was also great for me to spend some time with the younger members of my family.

As I played with them, I was reminded of all the knowledge children bring with them to a classroom.   They have an understanding of who has more or less.  They devise mental math strategies to keep track of the score during a game.  They can estimate how many lily pads are in the lake.   They can figure out how to evenly share 3 brownies with 2 people.   Most of this was not taught to them in school.

When I was teaching, I was constantly thinking about “prior knowledge” when I planned a lesson.  But I think I was somewhat misguided in what I believed prior knowledge entailed.  I thought it meant what the students had learned in prior years in school.  I didn’t think about what intuitive strategies or knowledge students already had from their experiences in the world.

I also didn’t consider how I could build on that in my classroom.  For example, their intuitive ability to share brownies among different numbers of people can be used to begin to teach fractions.

One group of researchers (see the book below) has documented the intuitive knowledge children bring to the classroom as well as ways to use this knowledge in the classroom.   It’s interesting to see how they foster new strategies and understandings by using what children can already do.

Thinking about how to build on what students can do instead of focusing on what they can’t do changed the way I approached teaching.

What about you?  How do you build on what children can do in your classroom?

Want to know more?

Read Children’s Mathematics: Cognitively Guided Instruction.


A mathematician’s lament

My favorite thing about Jo Boaler’s course “How to Learn Math” so far has been the assigned reading.  She assigned Paul Lockhart’s “A Mathematician’s Lament: How School Cheats Us Out of Our Most Fascinating and Imaginative Art Form.”  

I think this should be required reading for anyone who teaches math, supervises the teaching of math, or is a parent of a child learning math.

It’s a powerful piece.

He starts by describing a terrible nightmare a musician had.  In it, music is taught as math is in many of our schools:  as a collection of rules that must be memorized.  Students do not play or listen to music until after they have learned music notation and theory.

He then goes on to critique the current state of math education and claim that it is destroying the creative aspect of math by discouraging exploration and discovery.

Some of his suggestions are a bit unrealistic (just play games in math class) and some I completely disagree with (schools of education are a complete crock).

But I appreciate his ability to imagine what mathematics education could be.  I love his passion for mathematics.  And I love that he states so succinctly what we know from research about what many kids think about math: “They say,  ‘math class is stupid and boring’ and they are right.”

Years of research have show us that students have a great deal of anxiety about math and recent research shows this may begin at an even earlier age than we once believed.  Maybe Lockhart’s solutions are too radical.  Maybe they aren’t.  But it seems to me that doing the same thing that we have been doing won’t produce different results.

What do you think?

Want to read the book?  Click here.

Check out the some of research on math anxiety:

Vukovic, R. K., Kieffer, M. J., Bailey, S. P., & Harari, R. R. (2012). Mathematics anxiety in young children: Concurrent and longitudinal associations with mathematical performance. Contemporary Educational Psychology.

Exploring the hype about MOOCs

As I mentioned in a previous post, I enrolled in Jo Boaler’s course “How to Learn Math.”   The class began this week and so far I’ve completed the first session.

Ever since companies like Udacity and Coursera started offering these massive open online courses (or MOOCs), I’ve been curious about them.

I think it’s great that a large number of people–this class has about 20,000 students enrolled– from all over can access the material for free.

But the teacher (and researcher) in me wonders how the learning occurs.  I have the following questions:

  • How does the role of the student and teacher change (or not change) in an MOOC?
  • What are students learning by listening to lectures and answering questions?
  • Are online discussion forums with peers a sufficient substitute for an instructor-facilitated discussion?
  • How is the feedback that students are (or aren’t) getting fostering their learning?

That’s why I enrolled in the course.  I wanted to experience it as a learner so that I can begin to think deeply about those questions.

I also need to explore the research to find out what researchers are discovering about these courses.

I’d love to hear from you about your experiences in MOOCs.   What do you think?

The worst thing you can say to a student struggling in math

“It’s easy.  Let me help you.”

Ok.  Maybe that’s not the worst thing you can say to a student, but it’s up there. Yet, well-intentioned teachers and parents say it all the time. Why?

For starters, the problem is easy to us. We don’t understand why a student is struggling with something that seems so obvious to us. Second, we are often uncomfortable watching students struggle and sometimes, the quickest way to alleviate the discomfort is to show a student how to solve the problem.

So why should we avoid saying this to students?

It’s likely that a student could interpret it as: “If it’s easy and I can’t do it, I must not be very smart.”   This is the last thing a struggling student needs to hear.

In addition, offering help creates the misconception that math is not something students can make sense of on their own. Furthermore, the help you give may not address the real reason the student is struggling.

So what can you do instead of offering to show a student how to solve a problem? The research offers one solution– find out why the student is struggling by interviewing them.

“Tell me what you are thinking,” can be a good place to start. Maybe the student doesn’t understand the vocabulary or language in a problem. Or maybe the student is missing the prior knowledge that is needed in order to solve this new task.

Finding out why the student is struggling is a good first step. We’ll explore next steps in future posts.

Want to know more?

Take a look at chapter 3 in Van de Walle’s book: Elementary and middle school mathematics: Teaching developmentally.

Read Children’s Mathematics: Cognitively Guided Instruction

Check out this article about how one teachers tried this in his classroom:  Buschman, L. (2001). Using Student Interviews To Guide Classroom Instruction: An Action Research Project. Teaching Children Mathematics, 8(4), 222-27.

The Museum of Mathematics

One of the things I love about living in New York City is that I am constantly discovering new things about it.  I feel as if I could live here another 30 years and still not see all it has to offer.

The summer is always a great time for me to explore new parts of the city and visit places that I’ve been too busy during the school year to check out.

On the top of my list for this summer is the recently opened Museum of Mathematics.

Located at 11 East 26th Street in Manhattan, the museum boasts that it is “the coolest thing that ever happened to math.”  That seems like a rather bold claim, but it does appear to have some cool exhibits and activities that allow children (and adults) to have a variety of hands-on experiences with math.

There are activities where you can explore the Pythagorean theorem, fractals, and geometric figures.

Not having visited yet, I can’t comment on the learning that occurs from these activities.  However, I do think it sounds like a great way to expose students to math in a creative and fun way.  Perhaps something there will spark a child’s interest or alleviate his or her anxiety about math.

For those of you looking to prevent summer slide, it seems like a great place to take your children over the summer or to recommend to your students.

I will be sure to report back after I visit. I would love to hear from those of you who have visited it!

How can we prevent summer slide?

I hope you all enjoyed a nice long holiday weekend.   Since summer is in full effect, I thought it might be important to talk about summer slide–the loss of learning that can occur over the summer.

Research has shown that students lose skills over the summer, particularly in mathematics.    Furthermore, we know that this learning loss is cumulative and disproportionately affects low-income students.

Parents often ask me how they can prevent summer slide.  Here’s one suggestion: try a bedtime math story instead of reading a book to your children before bed.

Laura Overdeck has a neat website called bedtime math.  Her goal is to make the nightly math problem as common as the bedtime story.   The site posts a daily math story that you can read to your kids.   Included after each story is a series of math problem created for different age groups: wee ones, little kids and big kids.

I think the site includes some great stories and some fun ways to begin to make math part of your child’s daily routine.

I’d love to know what you think about the site as well as what suggestions you may have to prevent summer slide.

Want to know more about the research on summer slide?

Download this free e-book:  Making summer count 

Number Talks

In my last post, I talked about the importance of fostering mental math strategies in class.

A great resource for how to think about doing this in your class is Sherry Parrish’s book Number Talks: Helping Students Build Mental Math and Computation Strategies, Grades K-5.   I highly recommend taking some time to read the book over the summer.   It even includes a DVD with videos of model number talks.

So what is a number talk?

It’s a 10-15 minute conversation about a computation problem that is purposefully designed to allow students to communicate and justify their thinking.

What might it look like?

In the early grades, it might involve asking students for different pairs of numbers that add up to 10.

In the later grades, it might involve asking students for different ways to solve a multiplication problem like 25 x 16.

After sufficient wait time, students share their strategies, including justification for why a particular strategy works.

What I love about number talks is that they can easily be incorporated into a class.  Often, as teachers, we are bound to a particular curriculum that is beyond our control.  However, most of us can find 10 or 15 minutes to add in a number talk, even if it’s not every day.

I also love that they challenge different students.  Higher-level students can think of more complex solutions or multiple solutions while lower-level students can access the problem with a simpler solution.  And all students can benefit from hearing alternative methods.

Finally, I love that they allow for rich discussions to take place.  Students can talk about which solutions are mathematically correct or which may be more efficient.

Have you tried number talks in your class?  How have they worked?

Want to know more?

Check out this article:

Parrish, S. D. (2011). Number Talks Build Numerical Reasoning. Teaching Children’s Mathematics, 18(3), 198-206.