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10 Articles Categorized in "Mathematics"

Mark Gardner | Assessment, Current Affairs, Education, Education Policy, Life in the Classroom, Literacy, Mathematics | April 30, 2012

The English Problem

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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."

Rob | Assessment, Current Affairs, Education, Education Policy, Elementary, Literacy, Mathematics | October 30, 2011

NCLB 2.012

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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?

 

Rob | Assessment, Current Affairs, Education, Education Policy, Elementary, Life in the Classroom, Literacy, Mathematics | September 23, 2011

Testing the Limit

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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.

 

Mark Gardner | Assessment, Current Affairs, Education, Education Policy, Mathematics, Social Issues | August 19, 2011

The Skills Gap...again

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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.)

Visit msnbc.com for breaking news, world news, and news about the economy

 

 

Brian | Assessment, Education, Mathematics, Science | September 30, 2010

Would Value-Added be More Fair?

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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? 

Mark Gardner | Current Affairs, Education, Education Policy, Mathematics, Science | August 19, 2010

Should Math and Science Teachers be Paid More?

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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.

Mark Gardner | Life in the Classroom, Literacy, Mathematics | April 18, 2010

Basic Addition

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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.

Kim | Education, Life in the Classroom, Literacy, Mathematics | May 30, 2009

Knowing vs. Thinking

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I read an article a couple of weeks ago that really caught my attention. Unfortunately, when I went back to it - or at least TRIED to go back to it, I couldn't for the life of me remember where I had read it. Darn. It was about the use of technology in the classroom and how, if we aren't careful about how we use it, we might actually be doing more harm than good to our students' ability to think critically.

What technology and the use of the internet can give us is instant access to amounts of information so vast that our ancestors couldn't even have dreamt of it. Yes, I am a Google fanatic, and even as an English teacher who refuses to spell "relief" any other way, I have been known to use "google" as a verb. However, when I recently assigned my students a research project, I was reminded of how dismaying it is to see how they confuse "finding information" with "thinking" and "learning." They are great at cutting and pasting information into beautiful PowerPoint presentations or blogs or webpages. What this lost article pointed out and what I have fought against in my classroom is the ease with which technology negates the need to actually think. I require that for every sentence of fact, students are required to present two sentences of their own analysis, but often students are willing to settle for a lower grade in order to avoid the "pain" involved in activating their brain.

It reminds me of a conversation I once had with one of my daughter's elementary school teachers who felt it was unnecessary to require kids to memorize the multiplication tables or spelling lists because they would always have access to calculators and spell check programs. I tried to explain how understanding the concepts underlying the equations and word structure was just as important as being able to solve the equations or spell the words correctly, but she was in complete disagreement, stating that there are plenty of other areas where the kids can be asked to "think," and that if we skip some of the rote memorization, we can move on to more and better concepts. I understand the point she was trying to make, but recognizing patterns in equations or word formation is basic to analysis of any kind.

While we're touting the use of technology as "best practice," we have to be conscientious that we are not substituting flashy presentations and clever sound bites (or bytes) for true critical thinking, which is fundamental to the success of civilization.

P.S. If anyone read that article and could lead me back to it, I would greatly appreciate it!

Travis Wittwer | Assessment, Books, Current Affairs, Education, Education Policy, Elementary, Life in the Classroom, Literacy, Mathematics, Mentoring, National Board Certification, Parent Involvment, Professional Development, Teacher Leadership, Web/Tech, Weblogs | February 7, 2009

Stories from School now on Twitter!

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Do you want to receive your Stories from School posts through Twitter? Now you can . . . . 

Kelly | Mathematics | July 8, 2008

"Piaget? Is that like the French car company?"

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Sitting at an all-staff school improvement meeting, I wondered how I might bridge this apparent chasm in understanding about education.

A couple of years ago, I watched Eleanor Duckworth, an expert in child development who studied under Piaget, tease out three fifth-graders' conception of proportion using different-colored paperclips to represent juice and water mixed. One kid felt it seemed a little strange, but all three decided that if you had two green and two white paper clips, that was the same "juiciness" as one green and two white paper clips. Following the demonstration, a classmate asked if she ever saw children demonstrate understanding of proportion at an earlier age. "Oh no, it would be a debate even into high school."