Rethinking high school math

I came across an interesting article in the Delaware Cape Gazette regarding high school math. There were two things that attracted my attention:

High school Principal John Yore said teaching geometry at ninth grade is ideal. “The top scores come from students who’ve had geometry or better. Students who take geometry at ninth grade do better at upper-level high school courses and on any standardized test, including the SAT.”

In response, I would say, “Of course they do!” If you take geometry in ninth grade, you are far more likely to take an upper-level course, let alone do well at it. It is difficult – nearly impossible – to take a Calculus course if you don’t take geometry in ninth grade. One result of taking an upper-level course is a higher score on standardized tests; most college entrance exams  assess content through precalculus.

[One board member] asked if the district needed to address math at the middle schools, as well. Robert Fulton, high school education supervisor, said both middle schools already have math specialists. The priority is the high school, he said, which needs support.

So what do the math specialists do? Ideally, the specialists’ time is spent working with teachers, focused on effective instruction. But this isn’t enough. The board needs to be asking what systems have been put in place to address students that fall behind in middle school. Waiting to address problems in high school doesn’t work (I’ve been there).

In this case it’s about instruction, but it’s also about effective (and early) intervention.


Making Change: Part 1

I’ve been doing some thinking about the last post, regarding the need for change.  I was (intentionally) vague in stating how we need to change, although I had planned to address that issue later.  What I realize now is that this is way more than one post; here is part one of [who knows how many?].

Sometimes the systems in which we work are broken and need fixing.  One of these systems that deserves our attention is the options and support available to students who are below grade level in mathematics, particularly at the secondary level.  The reality is that all teachers should know more about the Response to Intervention (RtI) model besides the fact that such a model exists.

How do we provide for these students?  We must begin by understanding their individual needs.  Diagnostic assessment data provides one perspective and can help identify potential students .  Another important factor is teacher input; this provides a critical perspective about students who would or would not benefit from some type of intervention.  The system within a school or district needs to support the transition process and provide the opportunity for teachers – those who know the students at the individual level – to provide input into the intervention placement process.

Once we are aware of individual student needs, we need to approach the numbers of students – however daunting or discouraging – with a positive attitude.  Schools and districts need to find ways to accommodate the needs of these students.  The key to this system is increased time and intensity – “remediation” in the traditional sense will not work, because we are obligated to help students who are below grade level get on a trajectory that will get them to grade level proficiency (hopefully before they leave our buildings). 

The task, then, is to find a way to increase the time that these students are spending in mathematics – often through “double-dose” courses – with resources that are not changing and sometimes decreasing.  In most cases, this process involves a significant change in the way that schools and school districts do business.  However, this change to the existing system is necessary to facilitate further changes that will benefit the students whom we serve.

(Next time: Changing the way we think about instruction and instructional resources for students below grade level.)

The Whole Truth…

I had the opportunity to talk about assessment with a group of elementary school teachers earlier this week.  Our discussion focused on scoring, with particular emphasis on the scoring of constructed response items similar to those that appear on many state assessments.  In Colorado, there exists a set of holistic rubrics for this purpose.  They are sound, but require some understanding of what is being measured to be used effectively.  We also talked about preassessment – why and how to preassess kids.  This topic is better suited for a later post.

Knowing that this presentation was looming on the horizon, I had been on the lookout for assessment-related ideas anywhere I could find them.  So last Saturday, while enjoying a Shrekmarathon with my wife and kids, I found what was looking for.  In the first movie, Shrek overhears Fiona lamenting about her ugliness and thinks she is talking about him.  Dejected (he had just worked up his courage to express his undying love), Shrek walks off into the night.

I showed this one-minute segment to teachers.  Then I made my point: when it comes to assessing student learning, be sure

  1. you have the whole picture; and
  2. you have the right picture.

Sometimes, whether observing students working or scoring an assessment, it is easy to miss the big picture or to only get a part of the picture.  If we use assessment data to guide our instruction, but we’re working with an incorrect or incomplete picture, then our instruction will miss the mark. 

So next time you think assessment, think Shrek – and get the whole picture the first time.

On Conferences and Intervention

We recently concluded the annual conference of the Colorado Council of Teachers of Mathematics (CCTM).  This year and next, I am serving as the conference co-chair along with Ann Summers, a colleague from Littleton (Colorado) Public Schools.  This year’s conference went very well; we had almost 1200 attendees, a wide range of speakers, and a great panel of exhibitors.  We anticipate that next year’s conference will be even better.

The theme of the conference was “Best Practices in Mathematics: The Best Intervention for All Students,” a thought that is consistent with my belief that “quality first instruction” (or “highly effective first instruction”) is really the number one thing we can do help students.  If we want to significantly reduce the number of students in need of intervention, then good core instruction is the key.

Which brings me to my presentation at the CCTM Conference, “Middle School Intervention Based on Student Need.”  In the district I work in, we have implemented a double-dose intervention for our middle school students who are significantly below grade level.  My presentation summarized this program, from the selection of students to the course structure to the first-year data.  You can view the presentation here.

The bottom line with interventions in any school or district is that they must meet the needs of every student.  Finding the right combination of time, resources, and teachers takes time and careful planning.  It won’t be perfect the first time around, and maybe not the second; but anything we do to help students accelerate toward grade-level content – and proficiency with that content – will have an impact on those kids.