Musings and Strategies From the Teachers Next Door

Posts tagged ‘problem-based learning’

The Struggle is Good

If you haven’t yet discovered the Open Middle site, may I introduce you.  Welcome to the world of challenging, thought provoking problems.  Dan Meyer introduced this concept, creating problems that have a definite beginning and end, but have an “open middle” that creates the space for students to solve problems multiple ways.  The open middle is what I love about math, why math is so much more than learning a set strategy.  It allows for understanding based on how you think and how you understand numbers.  I have seen kids come up with strategies that I would have never thought of…oh, how I love those conversations.  For that reason, this site is a gift.

This past week, I used a fraction problem with my 3rd graders.  Here is it: (source:  Open Middle)

fraction_number_line from openmiddle

Students were asked to place 3/4 on this number line.

While I anticipated my students to be a little stumped by the fact that 3/3 would not be at the end of the line, I had no idea the level of difficulty this would pose.  I wish I had recorded all the great discussion that ensued.

They justified their position, even tried to form a coup and overthrow me, when I challenged them placing 3/3 at the end of the line.  Guiding students through questioning is an art that I am practicing daily and there were moments that I wanted to just break down and “teach.”  But then it happened….my favorite sound in the world…”Ohhh, I see it.”  First there was one, one brave soul that walked over to the dark side and placed 3/3 on the number line correctly.  She even grabbed a ruler, measured the distance from 0 to 1/3, and proceed to place 2/3 and 3/3 exactly in the right place.  As soon as she began to measure, the kids got so excited as they SAW it.

At this point, I thought it was smooth sailing.  Next came the true task of placing 3/4, so the first thing they wanted to do was place 1/2.  Perfect.  I loved how they were using benchmark fractions, and I was sure that their misconceptions were suddenly gone.  Well….here is how is actually went down.1:2

The black line is where one student placed 1/2 and the red is where another tried to emphasize and defend that 1/2 would indeed be placed there.  I used all the skills I learned in my acting class and asked them to talk about what they knew was true.  The told me that 3/3 was the same as one whole.  We discussed and discussed.  Finally, they did come to realize where 1/2 should be and eventually 3/4, but not without a clear struggle.  These are not kids I teach everyday, but they are bright students with a wonderful teacher.  I don’t know if it was because they have only looked at fraction number lines with ending points of 0 and 1, but this experience reiterated the importance of exposing students to problems in multiple ways.  If they cannot transfer the information they learned from one type of problem to the next, then their understanding is basic and needs to be developed so much further.  I’m reading everything I can get my hands on…I want to be the best teacher I can be…I want to challenge, push, equip and help students make  a rich web of connections.

Feel free to pass on any wisdom you have.  It takes a village…

TED Talk Tuesday “Math Makeover”

Math Minded

Do you have a go to place where you look for inspiration and innovation?  For us, it’s TED Talks so from now on, Tuesdays are TED Talk Tuesday. Here is our pick of the week.

In this talk, Dan Meyer clearly illustrates the difference between poor math instruction and math instruction that engages students in deep thinking while sharing how he develops real world questions and problem posing.

He states the obvious, that “Math reasoning is hard to teach.  The way we teach it in the U.S. all but ensures they won’t get it.”  We know that, we see it in classrooms often.  Are you wondering how successful you are?

Five Signs You’re Doing It Wrong

1.  Lack of Initiative – Your students are not self starters.

2. Lack of Perseverance – Your students give up, they lack grit.  If the answer is not immediately clear, they expect you to hold their hand and walk them through it.

3. Lack of Retention– You find yourself teaching, and reteaching, and reteaching.  It just doesn’t hold.

4. Aversion to Word Problems-They hate word problems.

5. Eagerness for a Formula…to solve said hated word problems.

We’re guessing you are reading this because you value education and you want to get it right.  You desire your students to excel and your instruction to create depth and understanding in those whose minds you’re shaping.  So why do educators find it necessary to go back to the old multiple choice stand by?  We’ve witnessed students answering multiple choice questions like nobody’s business, but change one nuance and they are lost.

Meyer makes a great point.   Have you ever faced a problem in which you were given all the information necessary to solve it… in advance? Or better yet been given several options to choose from…wisely? We haven’t either.

We were so excited when we saw this talk.  He breaks the development of good questioning down, starting with a picture and getting kids talking, bringing in math, as the kids see the need for finding ways to talk about what they see, and then having the kids pose questions that need answering.

The beauty of starting with a picture, or something that all kids know about, is that it levels the playing field.  One of his examples deals with filling a water tank.  He shows it and then asks kids how long it would take to fill it.  Kids see the picture and watch a video of it being filled.  Now, when they talk about filling the tank, every kid is on equal footing, even those kids that have decided they don’t need to talk about math, because someone else has the answer – every kid has filled something, so they have experience upon which they can draw.  He then takes guesses and writes them down.  He found that in the course of one semester, he could put a new problem on the board, something they have never see,n and the kids would have conversations about it.

The takeaways:

1.  Use multimedia in your class  -as often as you can, the best quality you can.

2.  Encourage student intuition – to level the playing field for all students.

3.  Ask the shortest question you can – and then let the other, more specific questions develop through conversation.

4.  Let students build the problem.

5. Be less helpful – knowing it will develop patient problem solvers.

“It is an amazing time to be a math teacher.”  We have the tools at our fingertips.

For more insight, follow his blog.


April and Diane




Children Make The Best Scientists

The inquisitive and curious nature of children make students the perfect scientists.  As educators, do we believe that is true?

Beau Lotto, a neuroscientist, has done some fascinating work using children AS scientists. (You can view his TED talk for the full description.)  The basis for his experiment is that children do experiments everyday through play.  They ask questions, gather information and make conclusions.  He went into a school and had the children ask questions that they wondered about bees.  From these questions, they worked together to design an experiment to see if bees could solve a puzzle and learn to fly to a specific flower within a specific pattern.  The fascinating part of this story is the students did the observing, the investigating, and the gathering of information.  Funny thing though, he mentioned that the greatest resistance he had in doing this project was actually the teachers.  The teachers didn’t think the kids could do it, AND they weren’t comfortable trying something that might not work.

That made me stop and question my own philosophy of education.  Do I hold my kids back thinking that I am protecting them from failure?  Do I hold them back because of my need for control?  Do I hold them back because I have lost my sense of curiousity?

I decided to jump in with both feet and see my students as actual scientists.  I showed them Blackawton Bee Project and spent time letting them ask questions about the world around them.

After talking about our questions, I let them choose a question they wanted to pursue.  The only criteria is that it couldn’t be googleable 🙂

photo 4 photo 3 photo 2 photo 1

We have been working on our projects for 6+ weeks now, about 1 hour each week.  And they have astounded me – not all, but most.  Here are a few of our topics:

  • Does your zodiac really match your personality?
  • Does your intelligence determine how fast you can solve a maze?
  • Can kids determine emotions by expressions?
  • Do all dogs communicate the same way?
  • Do all people taste food the same?
  • Can you really tell what a person is like from their Facebook profile page.

They designed an experiment that would give them information they could use to answer their questions.   For example, the girl curious about the accuracy of zodiacs, created a questionnaire.  She randomly listed the personality descriptions of each zodiac sign, without listing the zodiac name.  Then she had place for the person to write their birthday.  So awesome!!

As they worked, they asked tons of questions about gathering data, having a good sample, and as they worked on a way to clearly present their material, they have created graph, learned to use excel, and worked on presentations using many different formats.  They are having to learn what it takes to speak clearly, maintain interest, and draw conclusions.  So much learning has happened.

As a teacher, I am learning to be comfortable not knowing how things are going to turn out.  It’s making me better.  It’s making me comfortable with my own “failure.” And it’s transforming my class into a safe place with students can take risks without having it effect their grade.  I’m finding that disinterested students are now engaged and the quality of work has greatly improved.

How has your class improved over time?


Problem Based Math Resources

We are always on the lookout for great resources to share.  Here is a link to Problem Based Curriculum Maps for math grades 4 and up.  There is a curriculum map for each grade level along with a great activities that are ready to use.  Enjoy!

You’ve Got This!

You've Got This

Do you ever wonder if you have what it takes to make the transition to STEM? As teachers we are constantly being pushed toward the newest trend and expected in implement it flawlessly with few resources. Our creativity has been stifled, and our lessons have become bland as we seek to please the mighty test gods to order seek proficiency on our new evaluation. STEM, we think, is just one more trend that will be thrown away in few short years, so we keep our head down and just continue day in and day out without ever adjusting our teaching. Well, let me say, let me shout…. TEACHERS – WAKE UP! Our time as come. We CAN be creative, we CAN have excellent scores and we CAN infuse life back into our students. And here is how:

  1. Mistakes will happen…it’s ok. 

Our mistakes are not about a lack of ability. Mistakes do NOT equal failure. We have to change our thinking. Our mistakes provide fertile soil to model risk taking and an opportunity to teach students how to use “failure” as a way to learn.

  1. Learn to embrace problems.

STEM is all about problem-based learning. When you are planning a lesson, train your brain to identify a problem for the students to solve. It takes a paradigm shift and some time to develop, but once you start, it gets easier. STEM is so much more than simply a hands-on activity, it’s using problem-based learning to teach. It REQUIRES kids to think and it levels the playing field between different types and levels of learners.

If you don’t even know where to start, here is a free starter pack to help you get started.

  1. Restore the fun.

Teachers, we have complained too long about having to teach our curriculum a particular way. We have seen how it is inadequate and does not work. This is our chance.  Gone are the days when skill and drill is considered an acceptable way to teach. We aren’t trying to produce robots or regurgitators of information. We want students that love to learn and take initiative and let’s face it…facilitating and guiding students to learning something new is LOTS more fun than lecturing!

April and Diane 🙂



Aha Moment


Making the switch to problem based teaching has been a progression for me.  Each and every time, I’m amazed at how engaged even reluctant students are when faced with a meaningful problem.  We have heard this time and time again.  As teachers, we all want to connect with our students and guide them to thinking critically, tapping into their creativity.  At the beginning, it seemed to take  forever to plan a lesson.  I wanted to do it often, but my own excuses kept it from happening. You know what I’m talking about – not enough time and not enough money to purchase supplies.   I thought each lesson had to be an event, a memory maker that kids would talk about long after elementary school.  Well, I’m here to tell you I was wrong!  Once your thinking shifts toward problem based learning, the ideas just come…small ideas, meaningful ideas, teachable moments are birthed on the fly.

Here’s an example.  I’m teaching a small reading group (1st grade) while others students are working on various activities.  One particular boy (I’m sure you have multiple kids like this in your class) has such a hard time staying focused, he is incredibly energetic, and has a wonderful imagination.  I’m teaching and notice he is not doing anything productive.  I quickly call him over to redirect him and ask him about the book we had been reading together.  I asked him what the problem was in the book. He said that the King and Queen were trying to get the baby to stop crying.  Next, I asked him how he would solve the problem.  He quickly replied that he would sing the baby a lullaby.  Guess what I asked him to do…that’s right…I asked him to write a lullaby.  He RAN to get paper and pencil, sat down and wrote the cutest lullaby about Spiderman (hey, I gave him no criteria).  He was so excited to show me.  I even let him record himself singing it on my iPad.

It was short, sweet, based on a problem from his book, and he was completely engaged.  He left feeling like a rock star, which sure beats moving a magnet/flipping a card for being off task.


STEM….It makes you think….

“When we are successful, students think they are playing”     Jaime Punjabi

Amid the craziness of teaching day in and day out, in between surmounting the piles of papers to grade, the RTI folders to keep updated, and let’s not forget the classroom behavior that must be managed, have you stopped and wondered, “There HAS got to be a better way”?

We have been feeling this way for a while, trying to master the different programs that are introduced each year as we revise school improvement plans and try our hardest to prove that we’re making a difference. Except we really aren’t. Not really. Students are managed and we very rarely encounter major behavior issues. But they haven’t been engaged. Where are the kids that we envisioned while in school? You know, the ones who hang on every word, the ones who eagerly await the next assignment and give it all they have because they are eager to show how much you have taught them?

STEM changes this. By changing our teaching, we are changing our classrooms. We want to share what has helped to change our view of education today. We want everyone to experience the hope of change that STEM offers. We are on a journey to share everything we have learned and are learning every day in the trenches of teaching. We can change the face of classrooms. Although it is titled STEM, for us, we don’t care what you call it officially, all we know is that integrating all subjects through inquiry-based instruction coupled with technology and engineering provides a classroom where students are engaged, interested, and are becoming independent thinkers and problem solvers!

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