Author Archives: dawndup

About dawndup

I'm a seventh-grade math teacher who switched careers after spending nine years doing software engineering. I started teaching middle school in 2008. I'm entering my fifth full year as a teacher, and am learning more every day. Middle school teaching is the most challenging and rewarding job I've certainly ever tried. This blog is about my efforts to take on constructivist math teaching and do things quite a bit differently than I learned math, while making my students and myself into problem solvers... with a little flexibility and a sense of humor. The name "Ooh Guess What" has to do with the most common question asked in my classroom. The answer to this question will often tell me quite a lot about my students!

Blood Pressure

Imagine you’re a doctor. As a doctor, your responsibility is to improve the health of your patients, and so you sometimes administer some routine, standard tests to find benchmarks of your patients’ health. One such test tells you the systolic and diastolic blood pressure of your patients. It takes about 30 seconds to administer and can tell you early if there are warning signs that a patient isn’t thriving, or whether a treatment you prescribed is helping.

One year, you walk into an interesting new reality. All doctors must administer the same blood pressure test at the same time of year, as part of the accountability system for clinics, doctors, and healthcare administrators. You tell all of your patients to come to the clinic at the same time of day for the test. The test takes a total of 15 hours. Some clinics administer the whole suite of blood pressure assessments over the course of one week, where other clinics spread the process out over two or more weeks. All patients must be tested, and so make-up blood pressure tests tie up the clinic for another week after the tests are done. You’re very curious about this new blood pressure test, but you had no part in creating it, and even though you are actively administering the test, you’re forbidden from looking at the testing instruments or the patients’ results as they are in process. You take this rule very seriously as you know someone who lost her job practicing medicine for explaining part of the test to a patient. In fact, you need to remove anything from your office that would give any help to patients in understanding their blood pressure test, and if any patient discusses the test inside or outside the office, their result is invalidated. Their invalid result is then sorted with the rest of your patients’ scores.

It would be great to know the results of the blood pressure test right away, so you could make some changes to your treatment plans for some patients. Alas, you get the results after four months of waiting anxiously for this important benchmark of your medical practice. With quivering hands you open the results file and get two numbers for each patient you tested. You sort and analyze the data.

It’s pretty interesting stuff. As a rule, your patients had improvements in their blood pressure over last year. You wonder if other doctors saw similar improvements. One clinic across town is still on an improvement plan for having consistently unhealthy blood pressure readings for years. Ninety percent of the staff turned over and they got a new administrator. Blood pressure readings are improving slightly, but you hear the workload and stress have been unbelievable. The stakes are so high that you’ve heard rumors of clinics cheating and falsifying patient blood pressure data, major scandals that paint an ugly picture of your profession.

Although you are encouraged by your patients’ overall results, the clinic administrator wants you to meet with a coach to craft treatment plans for patients whose readings were unhealthy. Does our clinic need a nutrition plan or should we prescribe beta blockers for all? You wonder about individual patients. This patient probably just didn’t try very hard on the blood pressure test. Motivation has been an issue all year and you suspect there are emotional issues related to a recent divorce. That makes it hard to focus on a blood pressure test for 15 hours. Another patient would probably thrive with diet and exercise, but you wonder if there are genetic issues at play or a hormonal issue. You just don’t have enough information to create a treatment plan, so the session with your coach is difficult. She wants answers you can’t give her because you only have blood pressure numbers. It seems a little silly to have tested patients for 15 hours and get no actionable or diagnostic information, but this apparently is the new set of rules for doctors.

You don’t want to seem as if you’re against doctor accountability, but the process is frustrating. Blood pressure readings used to give you a quick snapshot of information. You would like to be able to use the blood pressure reading to guide further questions for coming to a diagnosis. It blows your mind that the blood pressure reading is now seen as an outcome instead of a data point in the picture of a patient’s overall health. That you and your administrators are actually making diagnoses, treatment plans, clinic personnel assignments, and long-lasting community health decisions based on a blood pressure reading. That a simple snapshot of overall health takes 15 hours over the course of days of secrecy and stress. If I’m testing a patient for 15 hours, couldn’t I have diagnosed and treated their actual problem instead of just getting one indicator? How can anyone be expected to practice medicine in this kind of environment?

Wait. I didn’t actually mean “doctors”, “clinics”, “patients”, and “blood pressure readings”. What I meant was “teachers”, “schools”, “children”, and “math and reading achievement scores.”

This is a picture of my classroom almost ready for standardized testing time. I’m not done covering every poster. I think it’s OK to share this because there are no testing items in the room.

A classroom almost ready for several days of testing

A classroom almost ready for several days of testing

It’s time for a teacher-led manifesto for what we really want and need in order to improve the educational experience for our kids. Some people may look back on this era and wonder why our educational system didn’t rocket to the top of the international charts after putting these reforms into place.  But if you have boots on the ground, you will not be one bit surprised. We work in a baffling world, friends.


Leave a comment

Posted by on May 3, 2014 in Trends in Math Education



I teach an “Accelerated Grade 7” math course which covers all of the grade 7 Common Core standards and many of the grade 8 standards.  As such, I teach any student who’s ready to take it – I have mostly seventh-graders, but I have a handful of sixth-graders taking it ahead of schedule, and a handful of eighth-graders who are moving along at a slower pace.

A few of the seventh- and eighth- graders have academic deficiencies to the point that I do not know what to do or how to teach them effectively. It’s keeping me up at night and I wondered if anyone had some advice for me. This is what I mean and what I’m looking for.

I have one student who has very little concept of place value. As in, he holds a centimeter ruler up to an object and tells me “I know it’s between the 5 and the 6. I just don’t know how to write that number.” The idea of tenths never really got there.

Several of the kids don’t have the concept of area as a measure of coverage of 2-dimensional space. They can count squares and work with whole-number areas if they are given a diagram with squares on it. But given an object’s dimensions with rational numbers, and asked to find its area or surface area – not at all sure what that means.

Given an equation, such as “3x + 5 = 17”, they don’t understand what the equation means so can’t even begin to guess what value of “x” would make it true. This is where we are, when the kids are 13-14 years old and about to enter algebra I.

I fundamentally believe in giving the kids access to math that will challenge them and help them grow, and I’m really frustrated – and it keeps me up at night – when we take a test, and the paraprofessionals who help in my class report to me that some students did not know how to even start, what to do, or what anything meant.

During lessons, what makes all of this phenomenally more difficult is that most will hide what they don’t know – pretending to write, hovering over their papers, asking for bathroom or supply breaks, copying answers from a friend, etc. I can only get a sense of where they are if I sit and interview the student, which as you probably can guess, doesn’t happen as often as I’d like.

You might have seen students like this before, you might not – what I’m wondering is what you have done that has helped you and the kids work past it. Please give me some ideas – how can I structure my lessons, how can I use the paraprofessionals and SPED teachers better, how I can systematically identify, help, and give feedback to kids who are working way, way below grade level in a grade-level math class.  What has even been partially successful for you?

Thank you so much in advance!!




Posted by on April 20, 2014 in Uncategorized


What it’s like to live Common Core

My Facebook feed is often populated with friends’ negativity about the Common Core State Standards. Common Core is turning our schools into data-run factories for mindless automatons. Common Core de-values correctness, making our kids sloppy and undisciplined. Common Core is too hard and makes kids cry.  Common core makes kids pee their pants. Common Core requires 108 steps to complete a division problem.  Hitler would have loved Common Core! 

I live the Common Core every day as a 7th grade mathematics teacher.  I don’t hate it. Actually, I really value what it has brought to my teaching. It’s been difficult and stressful at times, as new initiatives are, but I’m optimistic that it’s going to help me become a better teacher and my students become better learners. All of the links above make flawed assumptions about Common Core. I’m getting pretty familiar with the middle-school Common Core math standards, and there are some things you should know before you share that viral video.



The Common Core State Standards (CCSS) are a set of learning objectives.  They lay out what kids should know and be able to do at each grade level. That’s it. They’re goals.  They’re statements such as “Understand the concept of a ratio” and “Solve linear equations in one variable”.  There are many ways to teach kids to reach those goals. The standards lay out some of the ways but give kids and teachers quite a bit of freedom.  Thus, Common Core is not a curriculum, a mindset, a religion, a structure, or a test or a set of consequences for failing the test. It is a set of goals and that’s it. 

A common set of state standards was badly needed.  Statistically, kids get a vastly different level of education depending on the state in which they live (see slides 22 and 23 here). Our educational system has produced consistently poor results for decades, and for those that think the educational system in our day was just fine – it wasn’t. One in three adults lacks basic numeracy skills – we’re products of a subpar educational system that has stagnated.  Until recently, the educational standards for each state were almost all different, with some states significantly low-balling standards to make it easier to make adequate yearly process (AYP) for No Child Left Behind.  States were feeling pressure or even being required to adopt new standards without the financial resources to do it, and so pooling resources in order to come up with a common set of state standards made a lot of sense.  It was, and is, a reasonable response to start the course correction.  We need to raise the bar, and so we’re doing it together.



I live in the world of the CCSS for Middle School Mathematics.  Implementing the standards has been challenging and stressful and at times very confusing, and I won’t pretend to love the process.  It’s hard, and it will be for some time.  But there are big payoffs, and you should know that overall it’s going to be a good thing for public education.  As an example, my colleagues and I just finished teaching a unit on Ratio and Proportion.  When we started the unit, we looked closely at the Common Core standards to understand just what our students are supposed to do.  CCSS-M 7.RP.A.2a reads:

Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin.

We struggled for quite a long time with what that standard means and what evidence shows you understand it.  Is it enough to be able to answer questions like these, that show you tables and graphs and ask you to pick which ones are proportional?  



These questions technically meet the standard, but they feel like they don’t answer a bigger question of why proportional relationships are important. Why would you need to check to see if a relationship was proportional?

Our department chair suggested that a student might be asked about three recipes and might need to know if they represented the same recipe but scaled up and down, or if they were different recipes.



This is a good application of proportionality. Will these make the same syrup or different syrup?  Which is the sweetest? Students can explain their reasoning in multiple ways, by dividing to make unit ratios, by graphing, by making a table, or making a diagram – any of those strategies would show the student understands how proportionality works.  Our team felt we were starting to understand more about this thread.

We looked together for other examples and brainstormed how we could teach students about proportionality.  We found activities that would tie together multiple standards, where students could represent proportional relationships with equations. We talked about real-life examples where inexact measurements come out to be nearly proportional but not exactly – as in human body measurements, or this example about worms.


We discussed common misconceptions students would have and how to start addressing them, as with students who had a weak understanding of place value and didn’t know what to do with decimal ratios, or misunderstanding the relationship between fractions and ratios. We created our unit plan together, and found some resources from teachers in other states who were teaching the same concepts.

My point is that as we were using the CCSS to help our students become better learners, it was making us better learners. That exercise of working through the confusion around the standards was necessary and important. It still is, every day. The standards alone aren’t going to improve teaching and learning, so embracing the process is critical.

A feature I like in the CCSS-M is the list of Standards for Mathematical Practice. It’s a list of strategies that make us better mathematicians – there are eight of them, including “Look for and make use of structure” and “Attend to precision” and “Use appropriate tools strategically”.  It’s helpful to keep the list handy, posted multiple places in the classroom and tucked in your planner – so you can use it to identify strategies that will help students tackle tough problems. As students wrestle with open-ended word problems, they can be taught to be more mindful of pattern-finding, the use of technology, correct attention to an algorithm, estimation, and questioning themselves about the correctness of their equation or model.  I like having common language to help students identify their thinking strategies and be mindful of their use.  “You do a great job of coming up with a mathematical model, so where I want you to work is on really attending to precision and being careful of sloppiness along the way. Check the reasonableness of your answer when you are done. Does that answer feel right?”  These strategies can be systematically worked on. I like that the CCSS puts them front and center.



So living with the CCSS has made life harder, but has made teaching better.  However, here are some features of the Common Core in middle school that are big problems for me.  There is probably a misplaced standard here and there, and there are still too many concepts to teach and not enough time for all of it, but really those are small details that we can navigate around.  My larger issues with the Common Core standards are these.

1) Mental math and estimation play a role in Common Core, but it’s not emphasized enough. There’s an amassing body of evidence that shows that simply improving your “guesstimation” skills can really improve your numeracy down the road, and it really is a skill we should systematically develop from the early grades on. Give me a 6th grader with solid estimation skills and calculator proficiency over a 6th grader that can:

I don’t know that we need to ditch these skills but I wonder if the decision to include them was based on tradition instead of actual data.  I wonder if we’d get more bang for the buck if we focused on mental math.  I would like to see us question it more.

2) Technology plays a very small role in Common Core as well.  In all of the middle school CCSS-M standards, technology is mentioned exactly TWICE.  Adults use computers for math modeling.  It’s how society interacts with math. Middle schoolers should be using computers often to model with mathematics and should know how to get the results they want from technology. It’s the 21st century, people.

3) By the time you get to 8th grade, the standards are almost completely divorced from any notion of practical application. The standards claim to balance conceptual understanding, procedural fluency, and application. I feel the 6th and 7th grade standards are well balanced between the abstract and the practical, but the higher math standards have almost no application woven in whatsoever.  What a shame.  Algebra is extremely practical, especially with the modern modeling tools at our disposal today – iPads, computers, smart phones, and programmable graphing calculators. Computer programming is nearly universal in the job market and a very practical application of algebra.  Why is it left completely up to the teachers to invent applications of 8th grade math involving linear functions, systems of equations, and exponential functions?  They’re beautiful, abstract, and also darn useful. We can find a much better balance.  We’re setting ourselves up for another generation of “why do I have to know this?”


All that said, if we can get past the nonsense about fighting educational reform, if we can accept the premise that we really do have some re-thinking to do about how we approach mathematics in school, if we fully accept our role as developing critical thinkers, and if we can embrace the vast resource pool that’s just becoming available to use as Common Core comes online – we’ve got a good shot at making this thing work. There’s more to do in other areas, but this will start some terrific conversations.


Posted by on January 10, 2014 in Uncategorized


Hour of Code activities!

The Hour Of Code is such an exciting initiative and I am a HUGE, huge believer in coding because of the thinking it requires you to do.  I thought to myself how programming changed me as a mathematical thinker – it’s a powerful tool for math modeling.  It’s frustrating, but any excuses we ever had for NOT teaching it are quickly evaporating.  It’s no longer difficult and confusing for kids.  You don’t have to compile, link, or wade through cryptic error messages.  Some languages don’t even require you to type. It no longer requires software to install.  It’s no longer time-consuming and hard to find information on how to code.  Furthermore, coding has gotten sexier and more exciting. It’s colorful. It’s beautiful.  It gives you feedback instantly on whether your thinking is right or wrong.

Students present their first big project in groups.

Students present their first big project in groups.

I use Khan Academy and Javascript for coding projects in my 7th grade math class.  I like the colorful editor, the easy management of my classes, and the seamless integration with Google Docs.

For your perusal, here are some programming mini-projects we’ve done in 7th grade math you might consider for your Hour of Code – sorted by Common Core Math Standard.

7.EE.4 Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.

7.NS.3 Solve real-world and mathematical problems involving the four operations with rational numbers.

1.  Write a program that draws a rectangle and uses variables for the side lengths.  Calculate the area and perimeter of the rectangle and display them on the screen.
Video: Using Variables

Video: Expressions

(Clown WS that goes with the video: Clown WS)

Video: The task about rectangles

2.  Troubleshoot a program that creates a pep rally graph and averages the attendance at 4 rallies.  (Order of operations troubleshooting).  I called these my “Wreck-it Ralph” activities, where I presented students with a broken program and tasked them with fixing it.  This activity was really great and created some awesome mathematical discussion.

7.RP.1: Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units.

7.RP.2: Recognize and represent proportional relationships between quantities.

1: “Rates, Ratios, and Fractions:

2: “Population Graph” (Wreck-it Ralph troubleshooting)

7.RP.3: Use proportional relationships to solve multistep ratio and percent problems.

7.G.1: Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale.

1. Price of shoes (Wreck-it Ralph):

2. Enlarging and Reducing Snowflakes:

Video / extension: loops and snowflakes

Rich math tasks really take on a new dimension when they’re done in a programming context.  The feedback is instant, the visuals are rich, the numbers are never easy to work with, yet mental math and estimation are crucial to understanding if your results are reasonable.  Abstraction and modeling are inherent in these tasks and they force students to really understand the structure of the mathematics.  The students, though, just say they like it.  They say they can’t wait to learn more.  They say “I’m good at this.”  They feel like good problem-solvers and creative people. And you know what? They are.

"I'm good at this."

“I’m good at this.”


Posted by on December 10, 2013 in Uncategorized



This has nothing to do with the math classroom. I was just talking to my husband tonight about our engineering school experiences and I thought of this anecdote.

I declared a major in Computer Engineering in 1993. I had some computer experience – I was a gamer, I knew how to e-mail, and I’d done a few little projects in Atari BASIC when I was a young teen. This experiences gave me just enough confidence to get a good start in my classes and persist with the engineering program.  I had to take a class on computer architecture in which we learned assembly language during my sophomore year, and I really did like the class and felt I did pretty well.  There’s one lecture that stood out in my mind.

The professor had just taught us about a memory address in which you could store the address of ANOTHER location that would actually contain your data, so it was a reference to where your data was stored.  I was trying to wrap my mind around this concept – so wait, the address 0xAA7FFE43 might contain the value 0xAA5B3D22 which is the address of the place that actually holds your information and what? And a friend of mine, sitting near the back of the room, raises his hand and says “Is that like a pointer?”  And the professor thought about it and answered yes, it’s exactly like a pointer.  And heads all around the room started bobbing up and down, and many of the other (almost all male) students mumbled “oh, pointers” to each other.  I had NO CLUE what a pointer was.  I did not have any idea what they were mumbling about.  I wondered what kind of strange planet I had just been dropped on.

Aside from my middle school Atari BASIC tinkering, I really hadn’t done much programming.  It wasn’t offered as a course at any of my schools, and I busied myself with enough high school activities and AP classes that I didn’t leave much time for learning more programming. I never really thought about learning it at the time.  Many of my classmates had taught themselves C and had written complicated and even professional software by the time they were sophomores.

I’m not making any judgments or excuses, but I notice that more males make time for tinkering, inventing, and teaching themselves about computers on their own, as a hobby, than females do.  I wonder why?  I think I, and really any of my classmates, would have had an easier time in engineering school if we’d done more tinkering earlier.

At the time, it just wouldn’t have occurred to me that it would be fun to mess around with computers just to see what I could do.  I do from time to time now.  I wonder why I didn’t find it interesting then.  I wonder if that tinkering spirit gets a kid a little bit of an advantage if they major in engineering.

If there’s a problem statement in there, I wonder what the solution is.


Leave a comment

Posted by on December 4, 2013 in Uncategorized


Order of Operations via Computer-Based Math

Toward the end of our unit on rational numbers and rational number operations, my team worked to address standard 7.NS.3 “Solve real-world and mathematical problems involving the four operations with rational numbers.”  As I searched for problems that could be modeled via computer programs, I realized some of them also addressed standard 7.EE.2 “Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. For example, a + 0.05a = 1.05a means that “increase by 5%” is the same as “multiply by 1.05.””

I have been teaching my students JavaScript via Khan Academy as a way of teaching math.  Here is a list of some lessons I did on these two standards!

1.  Area and Perimeter.

First, a video on how to create and assign variables, and display text.

The students’ task: draw a rectangle and use formulas to calculate area and perimeter.

2.  The averaging problem.
As we got more into learning about order of operations, I thought about this idea as a way of modeling an “order of operations” problem on the computer.  I gave the students this program, put them into groups, and told them it did not look quite right.  I asked them to please troubleshoot it for me.


The broken “averaging” program. Click the link above to see the program, and you can look at the spin-offs to see some student solutions (many incorrect ones or “discussion starters” as I call them)


This activity was AWESOME.  Students noticed the bar for “119” was the same as the bar for “312” right away, and that was one of the errors.  Many of the students noticed that the average was not calculated right.  It’s an order of operations problem because my formula for the mean has no parentheses in it.  Students actually found multiple approaches to fix it, and this problem generated some great discussion.

3.  The Cricket Problem.

I posed this problem on the board: “Jennifer owns reptiles.  The lizards each eat 2 crickets per day.  The snakes each eat 6 crickets per day. The bearded dragons each eat 10 crickets per day. Jennifer wants to write a computer program to calculate the number of crickets needed for 1 week.  She has this so far.

var L;  // lizards
var S; // Snakes
var BD;  // Bearded Dragons
var C;  // crickets
Write a computer command that will calculate the weekly number of crickets and display that to the screen.”

Many students were extremely baffled by writing an expression that had variables in it instead of using numbers I gave them.  We did “catch-and-release” as a class several times before groups made sufficient progress.  Eventually a few different solutions came out of this.  Two are in this program.

Tony and Maggie’s two solutions modeled the distributive property, something I hadn’t even planned to come out of this.  We did not fully process the distributive property at this time, but focused on the expression and the use of parentheses and the order of operations.  It was a great discussion.  The lesson was great for many kids, but was out of reach of some at this time. I think often about how much I’m asking kids to reach out of their comfort zone.  This one might have been too far, but if I don’t ask them to reach at all, they will not grow.  I struggle with the “just right” balance.  More formative assessment would help me, perhaps.  And I could have built some background knowledge a little better.

4.  The Money Program.

The final mini-project in this unit was for the students to create a program that would use variables to represent pennies, nickels, dimes, quarters, and dollars – and to calculate how much money you had with those amounts of coins.  I got some good results from kids, but I also had many students that got stuck and stayed stuck.  Part of the problem, I know, was the amount of time I dedicated to this (it was a little over 1 class period, but that did not feel like enough time) and that it was the same program for everyone and thus had no creative component.  I did decide that we had to end the unit because the Ratio / Proportion unit was next, and that is more of a power standard than order of operations at this time.  Here is a skeleton of the Money Program.  The project had a lot of potential, and I might have taken it farther if it could have been more creative for the kids.  Maybe I should have had them invent their own money system!

Coming next: lessons and project for Ratio and Proportion unit!

Leave a comment

Posted by on November 25, 2013 in Uncategorized


Project-Based Learning via Javascript

I’m joining the maker movement!! I’ve been feeling tugged for a long time to teach mathematics using computer science – learning programming as a means to accomplish math goals.  Some of the factors at work are:

– The current math curriculum has been around since long before the computer, and the nature of mathematics in society has changed to become more computer-based.
– Millions of computer science jobs may go unfilled due to a lack of skilled programmers
– In our school district, in a tech hub of northern Colorado, a child can actually choose, in the year 2013, to never take a programming course beyond their sixth-grade tech class.  Ever.  They can actually opt out of learning to program.
– Yet students cannot opt out of learning to solve systems of inequalities with a pencil.  This seems backwards to me.
– My own understanding of mathematics deepened when I learned to program computers.

I made a promise to myself to incorporate programming into my common-core-based seventh-grade math class this year.  This is a heavy promise.  I am not teaching programming as an end in itself (even though I believe that is worthwhile).  I need to integrate the common core standards and teach programming with a purpose.  It is not easy.  Yet I was really proud of the first unit we did and the first unit project my students pulled off.

Our first unit was on congruence transformations.  I gave students the task of creating a computer program that created a design with symmetry.  It had to include two transformations, and they could choose from translations, rotations, and reflections.  They had to describe their transformations in a write-up and explain how they created them.

The platform I chose was Khan Academy’s Javascript. Any programming environment would work.  I considered Scratch, but eventually chose Javascript because of Khan Academy’s easy integration with Google accounts and the class management tools given to teachers.

Here are a few examples of the incredible artwork my students produced with computer programs.  It took several days but was WELL WORTH IT.  I was so impressed with the quality of their writing and their ease with using the difficult math vocabulary.  They really had to think hard about transformations to make their projects work, and the results were nothing short of amazing.

Student work from our programming project on congruence transformations!

Student work from our programming project on congruence transformations!

I didn’t expect the results to be as good as they were, frankly, but it turned out to be a great project not just as a way of introducing programming, but also to really understand congruence transformations deeply.

Here is the rubric I used for the project.

Khan Academy Programming Project

I would really encourage you to try it.  I’ve been emboldened to do more with computer science in math – the key being to hold on to the mathematical purpose behind it.