Doug McRae, a retired testing publisher, from Monterey.

Doug McRae

At its meeting next week, the California State Board of Education will consider eliminating the incentive for schools to offer a full Algebra 1 course to students ready to take Algebra by 8th grade. But removing this incentive would result in a de facto lowering of expectations for mathematics programs in middle schools, and lead to a significant reduction in the number of middle school students becoming proficient in Algebra. Do we really want to do this?

Perhaps it is best to view this issue from the perspective of a middle school mom who asked in an email several weeks ago: “With state board action adopting Common Core grade 8 math standards in January, will middle schools be able to offer Algebra?” She continued, “My son’s school will be offering the new 8th grade Common Core class next year but not Algebra. I’d like my son (who is a high performing math student) to take Algebra 1 in 8th grade. The middle school principal, high school principal, and high school math teacher have all said this is a better pathway for college prep.”

My email reply was: “Middle schools will have the option to offer Algebra. The State Board’s action in January made the Common Core standards for grade 8 the state standards for California, but those standards are not mandatory, and schools may deviate if they wish. Whether the Common Core for grade 8 is a better pathway for college prep is a contentious and disputed issue. I and others view Algebra in middle school as a more ambitious and rigorous pathway for college math and science, more competitive with many European and Asian nations’ curricula.

“We see that California has proven over the past 15 years with our ‘Algebra by grade 8′ initiative that half or better of our middle school kids are capable of taking and becoming proficient in Algebra by grade 8. For this group of students, we view the State Board’s action in January as a step backwards. A better policy would be a true two-pathway policy: Algebra for those ready by grade 8 and Common Core grade 8 math for those not-yet-ready for Algebra.”

At the State Board meeting in January, there were PowerPoints and much discussion on the value of a true two-pathway policy for middle school math.  However, if one looked at the standards documents approved by the board, there was no language to support the offering of a full Algebra course in the middle school grades, only a hint via a graphic that Algebra in middle school would be acceptable. Based on that graphic, it was clear that the Instructional Quality Commission, which advises the State Board on implementing Common Core, had plans for statewide support for instructional elements such as curriculum frameworks, instructional materials, and teacher professional development, for Algebra in middle schools. But the elephant in the room was whether (1) the assessment system, and then (2) the accountability system would support a true two-pathway policy.

Good intentions via instructional supports will be trumped in a heartbeat by one-pathway assessment and accountability systems. In the real world, what gets tested is what gets taught. And if accountability systems such as the API give equal credit for less rigorous and more rigorous pathways, then schools will gravitate to the less rigorous pathways to maximize their APIs. For policymakers to ignore these realities would be to operate with blinders.

Under the current accountability system, 8th grade students who don’t take Algebra in grade 8 are docked points, for purposes of API scores, on non-Algebra standardized tests. Next week, the State Board will consider the CDE staff recommendation to eliminate that distinction and remove a school district’s incentive to encourage students to take Algebra in 8th grade.

That step—treating Algebra and non-Algebra math the same for API purposes—foreshadows the State Superintendent’s position once Common Core is implemented, as early as two years from now. If in a few years the state, on its own, does decide to create a new Common Core-based end-of-year Algebra test, the precedent will have been clearly established to treat it and Common Core 8th grade math the same for accountability purposes. Meanwhile, the Smarter Balanced Assessment Consortium plan upon which the Superintendent and his staff rely heavily, does not include designing or developing an end-of-the-year Algebra test. Rather, the recommended new statewide assessment system would involve only a Common Core grade 8 math test. All students would take that easier, pre-Algebra test, without distinguishing or crediting those currently taking Algebra. With this scenario, it does not take a rocket scientist to conclude that what is emerging from the policy cloud in Sacramento is a lowering of expectations (or standards) for middle school kids ready to take Algebra by grade 8.

State officials assert that the federal Department of Education will not accept a true two-pathway system for accountability purposes. But that is not true. There are potential assessment and accountability designs that would support a true two-pathway middle school math policy for California. These designs involve developing a valid and reliable Algebra test that is linked to the Smarter Balanced Common Core grade 8 test, and setting performance standards for both tests on the common scale of measurement that links the two tests. At least one other state has used this design and gained federal approval for their program for NCLB purposes. A benefit of using this assessment system design is that it would provide logical weights for how much credit to give each test for accountability system calculations.

Unfortunately, the recommendation before the Board next week does not follow the common-sense strategy just outlined. Instead, it foreshadows a less rigorous approach. Kids not yet ready for Algebra by grade 8 should benefit, since the Common Core grade 8 pathway will be superior for these kids than their current instruction and assessment pathway, but at the expense of lowered instruction and assessment goals for kids ready for Algebra.

The State Board should rise above the State Superintendent and CDE staff recommendations, and support a true two-pathway policy for middle school math. The Board also needs to follow a strategic plan to align future statewide assessment and accountability programs to both pathways to fully implement a good two-pathway policy.

•••

Doug McRae is a retired educational measurement specialist living in Monterey. In his 40 years in the K-12 testing business, he has served as an educational testing company executive in charge of design and development of K-12 tests widely used across the US, as well as an adviser on the initial design and development of California’s STAR assessment system. He has a Ph.D. in Quantitative Psychology from the University of North Carolina, Chapel Hill.


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  1. Paul says:

    Frances, the questions that you pose are answered in “College Bound in Middle School & High School? How Math Course Sequences Matter”, a 2012 study by the Center for the Future of Teaching and Learning.

    Molly and Hurley, as a professional who has taught math from Grades 3 to 12, in some of the state’s lowest- and highest-performing schools, I have had just the opposite experience. The former principal at the middle school where I now work bowed to parent pressure and relaxed the standards for math acceleration. This year, for the first time ever, we are offering remedial services and awarding C, D and F grades to Grade 7 Algebra and Grade 8 Geometry students!

    As for the regular math track, we long ago discontinued Grade 8 general math and instituted 100% social promotion, so C, D and F grades were already common in Grade 8 Algebra. The study that I reference above uses real transcript data to show that students who attempt algebra before they are ready never recover from the experience.

    Yes, a Grade 8 Algebra option should remain available in middle schools. No, most students aren’t qualified for that option. We’ve got to dispel the irrational fear that ‘no one will want to marry you if you don’t finish Algebra I in middle school’. Completing algebra in Grade 9 leaves plenty of time for students to meet and exceed university admission requirements for math.

    1. Doug McRae says:

      Paul: There is no question there were flaws in the “algebra by grade 8″ initiative of the last 15 years. Your commnent shows some implementation flaws I think due to local level decisions. At the state level, the biggest flaw was not to establish curriculum frameworks and instructional materials and professional development for kids not-yet-ready for algebra by grade 8 until the mid-00′s, and then not to follow that up with a “pre-algebra” or “algebra readiness” test to match the instructional supports that were defined by the statewide curriculum commission (and approved by the state board) in the mid-00′s. One final reaction to your comment — it may well be accurate that “most students aren’t qualified” for a middle school algebra option in your district, but statewide the data says that at least half of the 8th grade enrollment is qualified to take algebra by grade 8.

  2. Paul Muench says:

    Not at all clear that school districts are listening to Mr. Kirst’s advice and having patience. Seems our district is already anticipating the change and plans to drop the accelerated math program for next year. I’ve heard that we will find out next week. I’m guessing that the district is waiting on the outcome of this vote. I suggest another way to have patience is not to make any changes at this time. Seems much more patient to finish the policy work before taking any action.

  3. Doug McRae says:

    El, Molly, Frances, Hurley: I fully agree with the sentiments in your comments. CA has shown we have a substantial percentage of our 8th graders capable of becoming proficient in a full algebra course by 8th grade. The state needs to support an algebra pathway in all schools for those kids. The IQC is promising to support the algebra pathway for middle school grades via the instructional elements they are preparing for eventual state board approval, including curriculum frameworks, instructional materials, and teacher professional development. The issue raised by my commentary is whether the state will fully support both pathways for middle school grades in their prospective statewide assessment program and finally in their prospective accountability system. From the details now available from SBAC and from the recommendation in the agenda materials for next week’s meeting, it does not appear the state is headed in the direction of supporting algebra in the middle school grades in either the prospective assessment or accountability areas. Thatsa the problem . . . .

  4. Hurley says:

    Given California’s reliance on STEM graduates for the success of our state and the recognition that we need greater, not fewer, STEM graduates, I would like to see whatever means necessary to encourage districts to offer accelerated math pathways for those students who are ready and able. Stifling these students in classes where the pace is set for those who cannot grasp these concepts quickly not only stagnates their progress but potentially stifles their interest in a subject where they could excel.
    And excel they do. Compared to their peers, the nearly 200 students in the accelerated math pathway at our local middle school–which (based on annual intake and/or proficiency testing)puts them in Adv pre-algebra in 6th, algebra in 7th, and geometry in 8th–generally test at 100% proficiency in these courses compared to a district-wide average of below 50% proficiency for the same grades in other math courses.
    As a STEM major myself, I applaud the ideas behind the Common Core Math Standards, as I do believe that greater depth helps students gain greater understanding in math, particularly as it becomes more conceptual in algebra and beyond. However, I would like to see, at the state level, a clear recognition of pathways–with relevant testing protocols–that would encourage districts and school to provide accelerated math programs for those students who are ready and able to excel in them and who will likely become the STEM innovators and workforce in our state.

  5. Hear, hear, el! Let’s look at that last paragraph again and take it to heart. Student outcomes are what count. Whose agenda is being served here? It doesn’t sound like it has much to do with optimal general education of kids.

    How well-prepared are California’s K-7th grade students to launch into 8th grade algebra? How many such students are there? How many California 8th graders successfully complete 8th grade algebra now? What does this mean for the math education of the general population of public school students? Once we know these facts, what then do we do with the information?

    1. Soquel Creek says:

      I’ve compiled links to California’s public school performance on the U.S. Department of Education’s National Assessment of Educational Progress (NAEP) tests in math, science, and reading.

      California Public Schools and Performance on National Assessments
      http://soquelbythecreek.blogspot.com/2012/12/california-public-schools-and.html

      At the 8th-grade level, California public school students scored below average–toward the lower end of the spectrum–but above Louisiana, West Virginia, Mississippi, Alabama, and Washington, D.C. public schools.

      NCES Snapshot of California 8th-grade Math
      http://nces.ed.gov/nationsreportcard/pdf/stt2011/2012451CA8.pdf

      NAEP State Results in Math
      http://nationsreportcard.gov/math_2011/summary.asp?tab_id=tab2&subtab_id=Tab_1#chart

      1. navigio says:

        About 7% of 7th grade CA students scored proficient on the Algebra 1 CST last year. About an additional 30% in 8th grade.
        Also, be careful with state comparisons on national tests, especially as it relates to longitudinal results. CA has had the largest demographic shift of any of the large states in the past 2 decades. It is very important to understand the impact this has had on overall ‘results’. For example, african americans had the largest increase in 4th grade NAEP Math and English results (among the largest states) over the past 2 decades, even while overall reading improvements were middling, and overall current math results are the worst among the large states.

        That said, even NAEP warns against using its data to compare states.. ;-)

        1. Soquel Creek says:

          You’re right that it’s difficult to exactly compare one state against another. However, California seems to consistently lag the others on NAEP. We spend less per student than the national average. We have much higher student-to-teacher ratios.

          The following report provides a more apples-to-apples comparison. It also shows that California, overall, lags in math and science achievement. No doubt, there are many centers of excellence within the large system.

          “Mega-States: An Analysis of Student Performance in the Five Most Heavily Populated States in the Nation”
          http://nces.ed.gov/nationsreportcard/pdf/main2011/2013450.pdf

          You are also correct about our shifting student demographics.

          “California Public School Demographics”
          http://soquelbythecreek.blogspot.com/2012/12/california-public-school-demographics.html

          1. navigio says:

            Page 4 of that first link also contains a good graphic on how those 5 largest states compare in demographic shift.

  6. Molly says:

    As a parent, I’m really worried that by the time my kids are in middle school, Algebra won’t be available for them. I do think that there may be good reasons not to require Algebra for all 8th graders, or penalize those districts that don’t have all their 8th graders in Algebra. Otherwise, we’ll continue to have kids failing Algebra in 8th grade and then again in 9th grade, when maybe if they get more prep in 8th grade they’ll fare better when they meet Algebra the next year (maybe). But at the same time, I do think middle school Algebra MUST be an option– and not just in the fancy suburban school districts, which I’m quite sure will retain 8th grade Algebra as an option, but also for more diverse urban or rural districts, such as the one my kids are in. I think it’s vital that districts not just be allowed to offer algebra in middle school, but required to offer it to those students who are ready for it. Or else it’s a huge step backward, and furthers the disparities in college readiness, STEM achievement, etc. I am quite sure that my kids will be more than ready for Algebra in 8th grade (if not before). Will it be an option for them? It should be.

  7. el says:

    I’m less concerned with there being “incentives” to offer algebra in grade 8 than to ensure schools are “able” to offer algebra in grade 8, especially for kids who have been on that pathway up to now.

    By “able” I mean able to make it work with the funding they have, with the assessments they are expected to ace, with the staff and schedule limitations they face, and all the rest of the pesky implementation on-the-ground details that may get in the way of a standalone 6-8 grade school or 7-8 grade school being able to offer algebra for the students who are ready.

    I don’t want kids pushed into math they’re not ready for; in high school, we already understand that there are different mathematical paths for kids. It will be good to accept that this truly starts in middle school and that kids need what they’re ready for regardless of the opinions of those in Sacramento or Washington DC.

  8. Michael Kirst says:

    Your information on SBAC is just wrong. I talked with CEO Willhoft of SBAC in person on Feb 22 ,and he said you are wrong. The grade 8 adaptive assessment will allow students to take grade 9 SBAC algebra.
    The accountability issues for math are not finished either, so there is nothing final in the meeting this month about grade 8 algebra.

    1. Doug McRae says:

      Mike: The commentary does not talk about taking algebra in grade 9, it talks about supporting taking algebra in the middle school grades (grade 8 or before). Willhoft is correct the SBAC adaptive assessment planned for grade 8 will allow students to take algebra in grade 9, no problem with that. Also agree that the accountability issues for math are not finished, but the precedent set if the board approves equal API credit for less rigorous and more rigorous pathways will be problematic when accountability issues for implementing the common core for middle school math are fully addressed. Doug

      1. Doug McRae says:

        Clarification, Mike: If what you meant by the grade 8 assessment will allow students to take a grade 9 SBAC algebra course, as I thought you meant, then yup I agree with that. If you meant that the grade 8 adaptive assessment will allow students to take grade 9 SBAC algebra test questions via its adaptive branching feature, then no that’s not what the grade 8 SBAC assessment will permit. The SBAC blueprint released last November indicates the item bank for the grade 8 SBAC adaptive assessment will only have test questions measuring the grade 8 SBAC content standards, and will not contain test questions allowing the branching feature to measure the full range of the grade 9 (or high school) SBAC algebra course. And the grade 9 SBAC algebra test questions SBAC is developing, per the email I got from SBAC staff in January, will not be included in any pilot or field testing and will not be the basis for an adaptive test developed by SBAC nor linked to the grade 8 SBAC test. So, that information is the basis for my assertion that SBAC will not have a test capable of covering the range needed for a true two-pathway program that includes both SBAC’s grade 8 common core and SBAC’s grade 9 algebra content standards. I’ve heard others say that SBAC’s adaptive tests will handle both options for a true 2-pathway grade 8 math program, but the details for SBAC’s test development plan do not confirm that speculation. Thus, if CA wants an assessment program that covers both parts of a true two-pathway program, CA will have to develop the full algebra part of that plan on their own, and the test scores on the underlying common scale covering both sets of test questions would provide the differential credit for accountability calculations rather than equal credit for scores based on only one of the two sets of standards and tests. Doug

  9. Michael Kirst says:

    This article is misleading and premature. SBE is not done yet with its policy making for algebra. SBAC adaptive assessment will be able to shift students to an algebra 1 level through the adaptive design in grade 8. The proposed action by the SBE in march is to eliminate the accountability link to the outmoded general math curriculum currently used for grades 7 and 8. McCrae does not mention that common core has elements of algebra in it in grades before grade 8, and is more demanding than current general math general.
    Many students who want to take calculus in grade 12, need grade 8 algebra. SBE is working with other states to develop this pathway. People need to have some patience, and not leap to conclusions from op ed pieces.

    1. Doug McRae says:

      Mike: I appreciate the SBE may not be done yet with your policy making for algebra in the middle school grades. That is why I chose words like “foreshadows” for my commentary. I’m hopeful the SBE will arrive at a position that supports both common core grade 8 and algebra for both assessment and accountability programs as well as the instructional elements of implementating the common core for the middle schools math.
      But, current information is that the SBAC program will not support algebra questions in its adaptive design for grade 8 — SBAC is developing algebra questions but they are not pilot testing those questions and not planning to produce a grade 8 common core adaptive test with the range to measure a full set of content standards for a full algebra course. This information is based on an email exchange with SBAC staff in January, which I’d be happy to share with interested parties. So, if CA wants to have an adaptive assessment capable of measuring the full range of algebra at grade 8, then either SBAC will have to change their design or CA will have to undertake that effort on its own. I appreciate that the specific action on the SBE agenda for next week deals with the outmoded tests for grade 8 and 9 based on outmoded content standards for grades 6 and 7, but the point of the commentary is that giving equal credit to less rigorous instruction and assessmant (i.e., the outmoded stuff) and more rigorous instruction and assessment (i.e., the current STAR algebra end-of-course test) invariably leads to districts putting kids in the less rigorous curriculum and assessment to raise their APIs — the same phenomena that we’ve seen with modified assessments with our special education kids in recent years.
      That the common core has elements of algebra before grade 8 and within the common core for grade 8 is true, but essentially irrelevant for this analysis — the comparison schools and districts will make in the future will be between common core grade 8 and full algebra for grade 8, and for that comparison common core grade 8 will be the less ambitious less rigorous pathway. (see chart for the sharp increase of Hispanics taking and successfully completing Algebra I over the past decade – a success that will be jeopardized by the new policy.)Thus, equal API credit for these two choices will lead to schools shying away from offering algebra in middle school grades. Thus, my point is that equal credit for the less rigorous and the more rigorous, as being recommended for SBE action next week with our “outmoded” curriculum and assessment, foreshadows where we are headed for the future implementation of the common core, and is a bad precedent for that reason. Doug

  10. navigio says:

    Any time I read about the ’8th grade algebra issue’, I cant help but think about what it is we are doing (or not doing) in earlier grades to cause this problem. There is probably nowhere where ‘achievement gaps’ are more starkly represented than in the middle school algebra issue. Independent of the valid questions Doug brings up, I really wish we could see this more as a question of multi-year curriculum and implementation strategy.