Category Archives: Teaching

Is the PhD worth it?

I’ve spent the past 6 years working toward my PhD.  And I’ve wanted to quit more times for more reasons than I ever could have anticipated.

But I’m in the final stages now. I’m editing my dissertation and getting ready to send it to my committee. I can almost see the light at the end of the tunnel. I’m so close.

Someone recently asked me if it was worth it.

Whenever I’m asked to do a workshop during school hours, I always think– is this worth taking teachers away from the students who so desperately need them? If I don’t feel the answer is yes, then I won’t do it.

I’ve asked myself the same thing about getting my PhD often. Is it worth it? Is the time I am spending writing a dissertation worth the time I could be teaching kids or teachers?

Every time I wanted to quit, it was because I struggled with that question  And every time, I eventually decided that it was.

I did take some time away from it over the past 6 years (against much of the advice I was given). I took time to teach, to coach, to do workshops, to blog, and to read about what you all are doing. It helped me to remember what this whole enterprise is about and that all the research being done doesn’t matter if it doesn’t affect our students and our teachers and our schools.

That said, I have learned so much over the past six years from engaging in research and thinking long and hard about difficult questions. It’s changed the way I think.   Which has changed the way I design lessons, the way I teach kids, and the way I coach teachers.

So yes, it was worth it.

So now what?

I can share with you all what I found in my dissertation and what we found in our larger research project. But what I think is more interesting is sharing how I use what I’ve learned from this experience to my work with teachers and students. So that’s the plan for now. I’m sure I’ll learn lots from all of you along the way.

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.


The Waiting Game: Increasing Wait Time


I’m from New York so it should come as no surprise that I am not very good at waiting.   As a result, I struggled (and still do) to give my students ample wait time during class discussions.

Apparently, I’m not alone.  In 1972, Mary Budd Rowe found that the silence that followed elementary science teachers’ questions and students’ answers lasted less than 1.5 seconds in classrooms.

Why is wait time, or think time as it’s also called, important?

Rowe found that there were many benefits for students when wait time was increased to 3 seconds or more.  These included:

  • A decrease in “I don’t know” responses
  • An increase in the length and correctness of responses
  • An increase in the number of students that participated
  • An increase in student achievement scores

From my experience in math classrooms, I’ll also add that giving students more wait time creates a norm about what is valued in math class.  Solving the problem quickly becomes less important than thinking and reasoning about a problem.  That’s the message I want to give students about math.

So why is it so hard to do?

For me, the silence was uncomfortable at first.  Three seconds feels like forever in a classroom.  I was worried that my students would get off task or become bored.  However, I found that if the questions were appropriately challenging, students would stay on task.  For those who solved the problem in a shorter amount of time, I encouraged them to think of another way the problem could be solved.  After a while, the students and I became more comfortable with the silence and wait time became a norm in our classroom discussions.

I’m curious to learn more about your experiences with wait time.  How long do you wait after asking a question?  What benefits have you noticed as you increase wait time?

Want to know more?  Check out these resources:

Rowe, M. B. (1986). Wait time: slowing down may be a way of speeding up!. Journal of teacher education, 37(1), 43-50.

Rowe, M. B. (1972). Wait-Time and Rewards as Instructional Variables: Their Influence on Language, Logic, and Fate Control.