Category Archives: Mathematics


Recently I read a New Yorker article about Brian Greene’s multimedia project, which paid tribute to some of Albert Einstein’s discoveries. It was launched on the centennial celebration of his general theory of relativity. Brian Greene is one of the more famous string theorists due to the popularity of his books which have included Fabric of the Cosmos and The Elegant Universe among others. He is a brilliant physicist and mathematician. In the article the author relates a story about Greene being set to the task of figuring out how many inches it is from here to the Andromeda galaxy by his father… when he was five. Not typical five-year-old work. Which then segues into a “consolation” for mathphobics that even Greene struggles to comprehend the homework assigned to his children in third and fifth grade.

“It’s all about strategies—‘Come up with a strategy’— and my kids are, like, ‘I don’t have a strategy, I just know it.’” Really? He has time for infinity, but can’t seem to piece together strategies for how students can learn to work with numbers? Continue reading

Adjunct Math Instructor right after College: What was that like?

Community collegeBy Maren Johnson

I had just graduated from college and I wasn't sure what I was going to do next: Graduate school? Peace Corps? I didn't know, and I needed an interim job while I figured it out.

I answered an ad in the local paper to be a math tutor for a nearby community college. I got a call-back after the interview—they didn’t need me for a tutor, but there were two math classes starting the following week—would I be willing to teach them? I was very surprised by the offer, but I thought, “What an opportunity!” and said yes almost right away.

And why was this community college willing to hire a 22 year old biology and French major, who had graduated just 4 days previously, to be their new math instructor? I perhaps should have done more inquiring–I knew nothing at that point about the ins and outs of education employment, and the world of being an adjunct instructor.

The job paid very little, but by living in the bedroom of a house I shared with some college friends, I was able to make it work, at least for the short term. I taught evening classes which ended at 9:00 pm, and then had to drive home across town afterwards.

With no office or regular classroom, I held “office hours” on some chairs near the building entry way, providing assistance to students with their math as crowds strolled by.

The perks of the job? I had interesting colleagues, and I did help a lot of students learn some important math.

This turned out not to be enough as I could not support myself. After two quarters as an adjunct instructor, I ended up joining the Peace Corps. At least as a Peace Corps Volunteer I would have health insurance. I taught math while I was in the Peace Corps, and then became a high school science teacher.

Why am I writing about this now? The adjunct issue has recently seen some federal interest. With a surprisingly humorous title for a congressional paper, the Just-in-Time Professor report, authored by staff of the US House Committee on Education and the Workforce, notes that 50% of all higher education faculty are now adjuncts. Other estimates put the figure at 60%.  The report states that these contingent or adjunct instructors have “no job security from one quarter to the next, work at a piece rate with few or no benefits across multiple workplaces, and far too often struggle to make ends meet.” I’m here to tell you from personal experience that is no exaggeration.

A full time adjunct might make only $21,000 a year, according to a recently posted article about the issue. The work performed by adjunct instructors is critical to our education system—they provide a foundation in basic skills to students who are pursuing two and four year degrees. Adjunct instructors deserve a living wage. It is shocking they do not receive one.

Are Schools Really Failing?

CompassesSome "discourse" about all the failing seniors in Washington State wants us to believe (using Washington as a proxy) that schools are continuing to fail.

This Reuters article seems to suggest they aren't, at least in terms of "closing the achievement gap." (Here is the link to the source data.) In the Reuters digestion, though, one key passage stood out:

The only scores to stagnate were the overall averages for 17-year-olds. While black and Hispanic students improved quite dramatically, the overall averages for the age group barely budged in either reading or math.

Peggy Carr, a federal education analyst, said the flat trendline among older students was actually good news.

More 17-year-olds with shaky academic records are staying in school rather than dropping out, which makes them eligible to take the NAEP exams, she said.

Even though some groups showed significant gains, the overall average was the same. My math knowledge tells me that if gains happened somewhere and the average stayed the same, some group's performance decreased. That decrease is being explained as a change in the survey sample–kids who otherwise would have dropped out are now part of the pool. Makes sense. That might figure in to the "high" number of "failing" seniors on Washington State math assessments. In that first article linked above, Randy Dorn even alludes to the fact that a priority in schools today is to keep kids from dropping out: keeping them in the system longer. This is a good thing, but does have an affect on our "data."

So, wait a minute. Where else might this matter?

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The English Problem

File3561335707875By Mark

For several years, my building has been identifying and aligning curriculum to standards–first state standards and now Common Core Standards–with part of this process being the identification of the Power Standards! each unit of instruction is to focus upon.

Simultaneously, we are gearing up for a new teacher evaluation system which figures heavily on a teacher's ability to define what his/her students' learning targets are and assess and document student progress toward those targets.

To an extent, both have been an uneasy fit for me as a high school English teacher. It is not so much in the philosophies underpinning these movements. It is that no one that I talk to seems to understand what I've started calling "The English Problem."

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NCLB 2.012

By Rob

In a comment on my recent blog post Tom asks: "How can we rewrite the federal education bill so that it actually helps student learn?" This is a huge question. The difficult issues of funding, evaluation, accountability, standards, and testing must be addressed in a politically feasible manner. I don’t know what is feasible but I'd advocate for these ideas-

Standards: I support national standards. As a population we are more mobile than ever and there should not be a drastic difference in the curricular content among states. This requires a level of monitoring and evaluation of states and educational systems. Currently this evaluation and monitoring is done by comparing the separate standardized tests in each state. Although these tests are given to every student multiple times throughout their schooling it is difficult to draw definitive conclusions since these tests vary in rigor and content. Our testing system needs reform.

Testing: Evaluation and monitoring of education systems is necessary for oversight and informed policy decisions. However this does not require the current two week assessment window, every child tested, a huge financial cost, lost instructional time, and enormous pressure on educators and students. Instead this should be done with a smaller randomized sample of students and less impact and intrusion on instruction.

Summative tests, currently the HSPE and MSP (sort of), are assessments of learning given at the end of a particular educational stage. Passing these tests is necessary for students to receive credits or in some cases progress to the next grade. Presently these are a part of a broken testing system. With rare exception, the students who come into the tenth grade performing far below grade level are the ones who are not going to pass the High School Proficiency Exam.

This idea isn’t new but I support summative tests at grade 3, 5, 8, 10, and 12. Students should not exit that grade until they are proficient. How can a fifth grade teacher instruct a student on comparing and contrasting an author’s inferred message when the student is struggling to sound out every third word? How can an eighth grade math teacher approach the Pythagorean Theorem with a student who struggles to multiply?

I’ve heard teachers say (myself included) I could teach 35 students if they came to me proficient in the previous year’s content. Let’s go with this idea-

It begins with half day Pre-K for all students and full day kindergarten. Before they leave kindergarten they need to know their letter sounds, numbers, reading behaviors, and should be able to read and discuss the events in a predictable text. Those who are proficient enter a first grade class capped at 24 students (35 is too many first graders for any teacher no matter how academically proficient the kids are). Those who are approaching proficiency enter a first grade class capped at 16. Those far below proficiency enroll in a class capped at 12.

Schools would use their ongoing formative assessment in grades 1,2,4,6,7,9, and 11 to reconfigure classes and to carry the model forward. The student who enters second approaching standard but exits meeting standard would enroll in the third grade class with the highest student-teacher ratio.

This model has imbedded funding implications. The schools with the highest performing students would have higher class sizes and would be cheaper to staff as long as they continued to maintain high student performance. The schools with lower performing students, ostensibly with underserved populations, would have a lower teacher-pupil ratio and would receive more funding.

This model is not without its challenges. Schools would need to take great care not to track students by providing some students with continual remediation while others engage in higher order thinking. I believe smaller numbers of students is important when serving struggling students in reading and math it is also important for students not to be ability grouped for other content areas.

Can somebody tell me why this wouldn't be an improvement? Maybe this idea isn’t ready to be written into law but couldn’t congress earmark some funding so some districts could try it?


Testing the Limit

ScantronBy Rob

Great investments have been made to collect and use data.  The role of assessments and use of student data has shifted and it has changed the nature of education.

The standardized test, Washington’s Measurement of Student Progress, is analyzed extensively to meet the requirements of No Child Left Behind.  It is used to identify schools as “failing to meet adequate yearly progress.”  It is used to rank-order schools.  New metrics which control for the impact of poverty use this data to compare effectiveness among districts.  This assessment comes at a great cost- financial, time, lost instruction, grading, and tools for analyzing.  The information gained from it could be found with a smaller sample size and at a lower cost.

The Measurement of Academic Progress (MAP) tracks student growth across a school year.  This test is completed by students on a laptop in a separate classroom.  Our technology and curriculum coach devotes weeks to setting up the computers, scheduling, and proctoring each class.  The list of goals compiled for each student is exhausting and includes standards not covered for months or years or, depending on the curriculum, not taught at all.  I am pleased when the assessment result matchs my analysis of the student but often it doesn’t.

I get very little actionable intelligence from the results of my MSP or MAP scores.  But increasingly I have to answer for the results. 

The emphasis on testing extends far beyond MSP and MAP.  Over the course of the school year my students must complete 32 mandated “common assessments” with the score recorded into a database.  How the scores are used I have no idea.  Increasingly these assessments feel more like an audit of my teaching than a tool for improving student learning.

Students also complete regular math and spelling quizzes.  This is an additional 85 assessments.  While these tests tie closely to the content they contribute to the culture of ‘no child left untested.’  My students are expected to demonstrate their proficiency 117 times throughout a 180 day school year.  They are second graders.  In third grade the assessment load will increase.

This certainly wasn’t my experience in elementary school.  It wasn’t even the experience of my students ten years ago.  And this emphasis on testing isn’t preparing my students for adulthood:  The last assessment I took was four years ago.

One form of assessment has been overlooked by policy makers and more attention should be paid.  It is the teacher’s ongoing examination of student progress and understanding.  Teachers use this information to inform their practice and to adjust lesson pacing.  It gives teachers an indication of what to re-teach or where to extend.  It allows teachers to identify struggling students while there is time to arrange extra support.  It requires acute observation and meaningful interactions with students.  This process is at the heart of teaching; it’s where the magic happens.  It happens every day… except when we're testing.


The Skills Gap…again

File000106140795 By Mark

NBC News ran a story last night about Siemens and their 3400 un-fillable jobs despite an abundance of job-seekers out there right now. The segment (embedded below) also featured small businesses who also have an abundance of openings–one owner noting something to the effect of "we can buy all the equipment we want, but it's no good if there is no one skilled to use it."

The piece discussed the "skills gap" between what the jobs require and what the prospective employees were trained for or capable of doing… and thankfully stopped just short of blaming American public school teachers for causing this, the failing economy, or current debt crisis in Europe.

The solution to the skills gap, according to the report, was more training (not testing) in math and science. Okay, that's fine. But how about training in skills?

Several of us here at SfS have beaten the drum about the need for more investment in vocational and career and technical education at the high school level. This got me thinking: what if we took every penny currently dedicated to statewide testing and test prep at all levels and instead invested it in vocational and CTE programming starting even well before high school? What about devoting funding toward funneling kids toward voc/tech speciality schools after high school instead of always talking about "college readiness" as if enrollment in a four-year is the only indicator of a school's success?

Alas, in a cursory search, I was unable to find clear numbers about the cost to taxpayers to adminster and assess all the state tests. Certainly, vocational and CTE programs can be quite expensive due to specialized equipment or facilities needs, but still, I feel like when we look at the problems facing the country, we're mismanaging our investment. 

One of the first and most important lessons I learned as a pre-service teacher was to examine the needs of my students and adjust my response, rather than just dish them a canned curriculum regardless of their needs. When I consider what our economy and country apparently need from public schools, it isn't kids who can pass tests. We need kids with skills… and report after report highlights that skills gap. Our schools apparently are not arming the emerging workforce with the tools they need to be successful.

Instead of using tests to punish schools for what we're supposedly not doing, why not fund programming to help schools do what we ought to be doing?

(Sorry about the ads in the video below. I usually open another window and check my email, but you can multitask however you choose.)

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Would Value-Added be More Fair?

by Brian TestFestLogo

About a year ago I wrote a post on the idea of using "value-added" as a tool in teacher evaluation.  The Seattle Times weighed in recently with an editorial endorsing it, and encouraging "retrograde union leaders" to quit opposing attempts to link teacher evaluations to student learning.  As a local union leader I cringe at being called retrograde, but I'm getting used to the Times anti-union bias.  I am not opposed to looking at student progress as part of an evaluation system. That makes sense. What I do think is important is that the weight placed on any test score used for evaluative purposes must be commensurate with our confidence in the reliability of the test.  In my high school last year 84% of the students met standard on the Reading HSPE, 91% passed Writing, 42% passed the Math portion, and 43% passed in Science.  In Reading and Writing our students did significantly better than the state average; in Math and Science we did slightly worse.  But look at those numbers.  Is it really reasonable to believe that the same students that do so well in Reading and Writing are so terrible in Math and Science?  Or to believe that somehow the language arts teachers in the state are far and away better teachers than their colleagues in math and science?  Is it possible that the tests might not be fair?  Isn't it possible that the bar has been set at the right level for Reading and Writing, and far too high for Math and Science? 

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Should Math and Science Teachers be Paid More?

CSX8EhBy Mark

An article in this week's Tacoma News Tribune points out that in the state of Washington, high school math and science teachers get paid less, on average, than teachers of other disciplines. The assumption–not backed up by research or widespread observation–is that math and science teachers are lured away to more lucrative careers in the high tech industry and therefore do not stay in teaching as long.

Besides that, this study by Jim Simpkins, Marguerite Roza, and Cristina Sepe and produced by the University of Washington's Center for Reinventing Public Education raises several valid points about teacher compensation. However, it is what the study does not include that concerns me most.

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Basic Addition

Z9sk1r  By Mark

I'm lucky that my 5-year-old son comes to work with me each day. His preschool is housed in the high school where I teach 9th and 10th grade. In fact, his classroom is literally across the hall from my 6th period and just around the corner from the room where I teach the rest of the day.

Not long ago, I went in to visit him and his peers during my plan period. He and his little buddies were sitting around a table doing a math worksheet. Two frogs on lily pads plus five frogs on lily pads makes a total of seven. Three frogs jump off and you're left with four. Good stuff for pre-K. Sure, an occasional finger was employed in these basic mathematical operations, but for the most part this computation was quick, confident, and alarmingly accurate for a bunch of pre-K-ers. 

I listened as the little folks' conversations about math escalated until those little five-year-olds were adding and subtracting frogs accurately up in to double digits, and I kid you not, I heard one boy talk to another about the "pattern" he saw that the numbers repeated, and yes, he used the word "pattern." He pointed out that if he added three to nine it made 12, and if he added three to NINEteen, it made 22, and if he added three to twenty-NINE if made 32. Good stuff…not every 5-year-old will get that, but it doesn't seem unreasonable that every 15-year-old should.

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