All posts by Jana Dean

I love teaching math because teaching math is teaching problem solving. I want all of my students to have the personal agency that comes from being able to solve problems. I have taught mathematics to teachers and to middle school students. Currently, I teach sixth grade in the JAMS program at Jefferson Middle School in Olympia, Washington.

Do We Really Have a Problem Here?

As a teacher, I usually favor spending money on public schools.  Our teachers union voted to walk out this coming Tuesday afternoon to ask for more money for our kids.  After the vote, however, I wondered how bad our situation really was. Compared to other states around the country, do we really have a school funding problem?  I found some numbers and after a bit of analysis decided to pose the same question to my sixth graders.

One up-to-date and reliable data set that I thought would matter and be accessible to middle school students was per pupil expenditures by state. I found it at the Kids Count Data Center.  It made sense to use these numbers because a data set of fifty is manageable and the sixth grade learning sequence demands understanding of distributions, box plots and quartiles.  The class was in its third day of a statistics unit.

Annual Per Student Spending by State, Data Source: Annie E. Casey Foundation, Kids Count, Generated by Alcula, Click to enlarge.

I proposed to the class that they would be using statistics to decide for themselves whether or not they agreed that their teachers should walk out to demand more money for schools. I passed out forty-nine numbers on index cards:  one number for each state.  I held our state of Washington face down in my hand.  I told them that they were holding one, two or three states in their hands and that the numbers were in thousands.  I didn’t write the names of the states on the cards so that the curious could ask about the states they held.  One lay way outside the bulk of the numbers, drawing envy and attention to the state of Vermont which spends close to $19,000 per year per student.  The class quickly determined that Utah had the lowest spending at a little under $7,000 per year per student.

I showed the five number summary I had calculated in advance:

  • Minimum:  7
  • Maximum: 19
  • Median (or middle:) 10.5
  • 1st Quartile (middle of the bottom half:)  9
  • 3rd Quartile (middle of the top half:) 13.5

I stood in the middle of a line on the floor and proclaimed myself the median (the middle number when numbers are arranged in order,) and asked everyone who had a card below the median (in the bottom half) to place it on the floor.  Then those between the median (middle) and third quartile (the top fourth) of the states came forward to place their cards.  Finally, I stood at the third quartile and asked the big spenders (the top fourth of the states) to come forward.

Then I stepped out of the line and asked if anyone had any questions. Hands shot up as several students blurted, “Where is Washington?”  I said, “I am still holding that card. Where do you think we belong in this distribution?”  A few pointed to the minimum, assuming that we keep company with Utah, but most pointed to near the middle of the line.

I stepped forward with my card with the nine on it and stood at the first quartile which marks the top of the bottom fourth of state spending.  I asked students what that meant.  They replied with dismay, “Three-fourths of the states spend more on kids than we do.”  Then I stepped out of the line again and took my place just eight states from the bottom.  I said, “Yes you are right, and with a total of about six states spending around $9,000 per student, we are about eight states from the bottom.  Do we have a problem?  Talk to your partner about whether we have a problem.”

I didn’t ask students to write down their replies because I want them to be free to decide for themselves if Washington State has a school funding problem. I decided that asking them to share would put them too much on the spot. The pressure of writing something down didn’t feel right:  It is my job to provide information, not to persuade.

When they shared out, most agreed that we have a problem.  One pair dissented and wisely said, “We think we need more information. It depends what they spend the money on, like tests or teachers or field trips or sports.”  I told them that another data set I could have brought was teacher salaries. “I am fine,”  I said, “but a beginning teacher makes the same hourly wage as my eighteen year old son does building trails in the state forest.”  Another student made the argument that his grandma was a teacher and things must be fine because she has good retirement, but then he caught himself, “Wait, she lives in Vermont.”

I agree with the pair of student skeptics.  We do need more information. How districts spend the money does matter.  But without the money to spend, those closest to the students — the principals and the teachers — won’t even have the option to choose to spend wisely.  I don’t plan on moving to Vermont, but I do know my talented student teacher is leaving the state for Oregon, where spending is near the median.

I don’t know how many families will join us on Tuesday, but the parent volunteer in the room was swayed by the data to reach out via email to the families of my class.  For those willing, let’s meet at Percival Landing at noon, Tuesday, May 26, all dressed in red and walk to the Capital Building for our kids!

(Un)Fighting Standardized Tests

I teach sixth grade and I find the MAP (Measures of Academic Progress) standardized test frustrating. Schools use it in ways I wish we didn’t and we can’t use it in ways we wish we could.  I didn’t realize how conflicted I really felt until my students bombed the test when I had them take it ‘just for practice.’ 

Learning Testing

I had asked that my students be excused from the second of three yearly rounds of testing. When I made my pitch to my principal, I explained that I can’t really use the MAP to inform my teaching because the information I receive from it is so generalized:  it doesn’t help me pinpoint what students know and don’t know.  Also, many of the sixth graders in my class read too much into their score and lose confidence in themselves as mathematicians if it doesn’t rise dramatically.

We decided on a compromise:  Take the test, but tell them it was just for practice.  Students wouldn’t freak out. And they wouldn’t lose out on a opportunity — and this is the part of how we use the test that I don’t like —  to experience how the school would determine their math placement for the coming grade.  They’d just calmly give it their best. Was I in for a surprise.

When I saw their scores, my heart sank.  They relaxed, too much. Much of the class didn’t do as well as they did when they took the test in fifth grade, in spite of six intervening months of learning. These results were completely out of line with every formal and informal observation I’ve made of their learning so far this year.  They also don’t match students’ performance in prior years and I have some of the most powerful student growth I’ve ever had this year.  Also the experience was still toxic, at least for some of them. One student came into class the next day begging to be taught algebra so he could do better next time.  Another was frustrated that she couldn’t explain her answers.  She loves that part of how we do math.   A third said it was a waste of time because he didn’t care about the MAP because tests like that aren’t going to determine who he is.

To learn more about what happened, I gave my students an anonymous survey.  Their responses to my questions and our discussion shed light on the results.  Here is what l learned:   When they know that a test is tied to an opportunity, like getting into a class, they do their very best. In fact that is what 80 % of them had done in fifth grade when they knew the test would determine their middle school placement. This time, for the practice test, about seventy percent of them reported not working very hard, because, they reasoned, “Why bother?  It was just for practice.” This was about the same percentage as those whose scores dropped.  They also said they wouldn’t ever work that hard if it was just practice. The test taking experience is unpleasant, it takes too long, and no one reads their work anyway.

My sixth graders taught me that what students understand about how test results are used matters to them.  They knew that in the 5th grade, their placement in math class would be determined by their score on the MAP and they responded accordingly.  I, along with many educators, have mixed feelings about this, and wish that students’ opportunities weren’t determined by test scores alone. In fact, as professionals with the best interest of children in mind, we can and do work with families to find the best fit for students. Sometimes, we can advocate successfully for a child who hasn’t scored well.   In the past I have shared this with students, emphasizing caring adults’ role in advocating for them.  But in reality those conversations are the exception, not the rule.  Usually it’s a score that determines a child’s math placement. In their world, the numbers do count. Test results matter to students’ future selves. Many of my students will find that doors open for them when they perform well on standardized tests.  Others will lose opportunities when they don’t do well.

I have gone into test days too wishful for years, and my wishes have skewed the way I present the experience to my students.  I look at the scores and wish I could learn more about my students from them, and I wish the scores didn’t impact my school and students so much.  My first wish is silly.  I already know what I need to know from spending day after day with these young people.  As for the latter, I suspect my nuanced understanding of human development as far more than a test score has been getting in the way of my students’ performance.  On test day, I have reassured them that I know how smart they have become through their hard work.  They believe in my belief in them and probably trust that I will be there if they slip up like I have been before.

Next time, instead of reminding them of how much I care about them, I will help them see the doors that open and close based on their scores. I will tell them that doing well means having choices and having more power and agency to determine the next steps in their own lives. I will tell them that I care about their results because I care about them. I will help them see that the tests are the only way that people who don’t have the time to come into our classroom and listen to how amazing they are can find out what they know.  To the extent that I can, I will help my living-in-the-present eleven year olds see past the people they already know to imagine those they don’t know yet and to have those people, including their future selves, matter.

Solving Problems that Matter

Math class goes like this: Teachers give problems; students do problems; teachers give the answers.  Teachers give more problems; students do more problems; teachers give more answers. Repeat.  Eventually, students get a grade. And then they know if they are good at math.  My students know this is how it is by the time they start middle school.  But in my class it doesn’t work that way.  Sure, I give problems, and yes, students do problems. And I have answers, but I keep them to myself. Knowing their answers make sense has to come from students themselves. My job is not to let them know whether they are right or wrong, but instead my job is to convince them that they have power and control over their own problem solving.

This may seem strange.  You may wonder, “How will the students know they are right if the teacher doesn’t give the answers?”  Here’s what I wonder “The last time you had to figure something out, how did you know you were right?”  I’m guessing you probably didn’t find someone in a position of authority and ask them to look it up in an answer key to confirm that you are a good problem-solver.  Genuine problems come our way without solutions.  If we had solutions, they wouldn’t be problems.  I’d be willing to bet you did one of the following as you solved the last problem mattered to you:

  • You didn’t what do do and you talked it over with your friends.
  • You slept on it, hoping it would go away and woke up ready to work on solutions.
  • You had an idea, tried it out mentally, and satisfied it might work, you took action.
  • You had an idea, shared it with a trusted friend or co-worker or family member to make sure it made sense to them too, and if it didn’t, you adjusted accordingly.
  • You tried your solution, saw it didn’t work, learned from your mistake and tried something else instead.

My math class offers students the opportunity to do what we all do when we have problems.  And if they knew I would provide answers as soon as they get stuck, the game would be over.  They wouldn’t that they are in charge of solving the  problems that matter to them.

Blue Brain


Brain research now confirms that deep conceptual learning requires making mistakes, and that the more positive we feel about mistakes, the more we can learn.  That’s because brain freeze, or what my sixth graders have started calling “blue brain” is real.  Many of my students have such an aversion to making mistakes that instead of digging into new ideas, they become paralyzed, hoping not to make a miss-step instead of trying out new ways of thinking.  I can see why. For sixth graders new to middle school the stakes are high: new friends, lockers (and combination locks), crowded, confusing hallways, five or six teachers, lunchroom rules, free time at lunch but no recess, PE and band lockers, binders, dividers and pencil pouches.  It’s a lot to keep track of and they don’t want to miss out on anything or be the focus of negative attention.  Some of them try so hard to get it all right that they have a hard time doing what they are at school for to begin with:  learning.

This year, about one third of my students tell themselves they are bad a math if they make a mistake, and more than half feel negatively about math mistakes.  If my students are going to grow to the greatest potential they need to break out of this mindset. They need to change their minds about mistakes and learn to see them as learning opportunities, even though the pressure they feel to succeed works to convince them of the opposite.

Luckily, in spite of all their efforts not to make a mistake, they are making mistakes anyway. And they don’t feel happy about it yet.  Rather than forcing them to feel happy, in our class they have started to call the uh-oh feeling you get when you make a mistake ‘blue brain.’  They got the idea of blue brain from a short BBC clip that shows the stop in brain electrical activity following a mistake as blue, and then shows the powerful mistake-fixing activity that follows as red.  The end of the video contains just fifteen seconds on the difference between positive and negative reactions to mistakes, but that was enough to support students to come up with the following list of things they could say to themselves to recover from blue brain more quickly.

  • Try harder next time.
  • Gosh I made a mistake, I’d better fix it.
  • It’s okay everybody makes mistakes.
  • I am learning.
  • Try again.
  • Keep going!
  • I’m just getting smarter.
  • Don’t feel bad, just fix it and move on.
  • That is okay!
  • Keep trying.  You know you can do it.
  • Mistakes make me smarter.
  • I will get it next time.
  • No one is perfect.
  • I’m just learning a whole new way!
  • That’s ok. It’s part of learning.
  • Now you can learn from your mistake.
  • So what?  Just fix it.
  • It’s not the end of the world.
  • You can’t learn without making mistakes.
  • Oh well, I will get another chance.
  • You can bounce back.
  • Let’s find a solution.
  • Don’t worry.
  • We can always try again.

As we enter the second full week of school, most of them aren’t yet happy to have the opportunity to fix mistakes, but at least they are beginning to have some tools and language to help themselves get back into the learning action as quickly as possible.