“These Standards are not intended to be new names for old ways of doing business. They are a call to take the next step.“ (Page 5 CCSS for Mathematics)
Educational Goals & Graduation Requirements – “All standards without a (+) symbol should be in the common mathematics curriculum for all college and career ready students.” (Page 57 of CCSS for Mathematics) If No Child Left Behind goals of universal college preparation are maintained and high schools strictly adhere to the CCSS for math, then additions will have to be made to the current math curriculum. It seems likely that graduation requirements will be impacted if all non-plus designated standards are adopted for all students. Department staffing and budgets will have to be increased to implement these proposed changes.
CCSS, An Unfunded Mandate – At a time when nearly all schools struggle to maintain the status quo budget wise, the common core reforms impose increased costs for staffing, hardware, software, classroom furniture and expanded course offerings. It’s hard to see how some adjustment of the timeline will not be made given the austerity measures currently being proposed in Sacramento.
Statistics Raised to Equal Status With Algebra & Geometry – Examination of the new CCSS clearly shows that statistics has now been recognized as a major area of math content that all students must learn in their high school careers. A review of the CCSS standards shows that approximately one-fifth of the volume of content is devoted to “Statistics and Probability”, and when one considers the new “Modeling” domains that closely align with topics traditionally taught in a Statistics course that proportion increases to one-quarter. Note that two of the six sample questions from the latest Showcase 3 materials were in the “Statistics and Probability” domains.
In a high school setting, the statistical standards not typically addressed in the core math curriculum are “Interpreting Categorical & Quantitative Data” (S-ID, #1-9); “Making Inferences and Justifying Conclusions” (S-IC, #1-6); and “Using Probability to Make Decisions” (S-MD #1-7). Presently at most schools, these content standards are only taught in AP Statistics. Some but not all of the standards listed in “Conditional Probability and Rules of Probability” (S-CP) are presently taught in a couple sections of one chapter in Algebra 2 textbooks.
Common core implementation will require that statistics is recognized as an important domain in a 21st century classroom. Properly implementing these standards will require that students take a statistics class. This additional course should have an application emphasis with substantial cross-curricular integration. Some educators may wish to maintain the status quo and recommend simply teaching an additional “unit” in these topics, or to absorb this statistical content across the three traditional core subjects (Algebra 1, Algebra 2 and Geometry). In assessing this view consider that many math teachers do not like or are not prepared to teach statistics. This view is to be expected since the practical utlity of statistics has only blossomed in the last decade with the phenomenal expansion of computational power and the breadth of data collection now common in the economy.
Acceptance of statistics' increased role may take time. Even the CCSS makes several references that could be read to imply that statistics lies outside the broad category of mathematics. If one does accept they are different, then it merely provides further support that statistics be taught as a separate course not as a part of another course.
Expand Use of Excel in Math Classrooms – CCSS and Smarter Balanced Assessment Consortium materials specifically reference spreadsheet and computer applications many times throughout. Notice that one sample question actually requires the students to do some of the work in a simple spreadsheet. “Functions” have now been identified as a major category of math with domains on its own. Excel formulas are an excellent tool for teaching functions cross curricular, particularly in science and mathematics. Excels’ function screens scaffold the mathematical process, and offer lower achieving students a clearer understanding of inputs and output. Excel’s graphic displays are another resource for deepening student understanding of how to apply their knowledge of graphing learned in Algebra and Geometry. Excel further offers great potential to assist students in mathematical simulations and modeling that are now a major part of CCSS and the proposed high stakes summative exam.
Increased Time Devoted To Testing – As I read it, the computer adaptive testing (CAT) program envisions a series of voluntary periodic assessments that lead to a mandatory summative assessment at the end of the year. For higher grades, some of these periodic assessments take the form of “Performance Tasks”. Per the Smarter Balanced Assessment Consortium Showcase 3 Materials, “It is true that some performance tasks will require both extended amounts of time (up to 120 minutes) and resources beyond the online tools that are part of the delivery system. The time allotted for performance tasks typically increases as students get closer to entering college and/or career to better reflect what is demanded out in the field. However, the time and resources required of the teacher/administrator will be minimized where feasible.”
Periodic assessments will need to be integrated into the teaching calendar. Such foundational changes often increase friction between the major components of school leadership. Every administrator, department chair and teacher will have divergent opinions on how to implement these periodic assessments. Many teachers will see this entire program as an imposition, and will resist implementing it. To avoid having reform efforts being derailed, schools should pilot changes with volunteer teachers initially. In some cases, thematic programs may be more philosophically comfortable with the common core’s emphasis on application, and may have a head start with integrating math instruction with other areas of content.
Computer Access – As proposed, the summative assessment will be computer administered which will prove a monumental challenge for an education system where resources are insufficient to meet the current challenges. At larger schools of several thousand students, test administration will no longer be campus wide. The regularity of the proposed periodic assessments probably means these assessments must be conducted in regular class sessions. That leads to a need for classrooms to be modified to accommodate the technological needs of implementing the assessments and preparing students for these assessments.
Reconfiguration of the Classrooms - For students to achieve on the new common core assessments above, the present stock of computers will need to be upgraded in numbers and quality at most schools. The summative and periodic assessments will also create urgency for expanding bandwidth. Calculators will continue to be used in math courses but instruction should transition toward computer applets and spreadsheet technologies. Computer applications are directly referenced in the CCSS, are the new proposed delivery mode of assessment, and will more directly link the learning of our students to the computational tools used in the workplace.
Potential to Widen Performance Gap – The test has added a substantial amount of math content to the standard curriculum without an equally offsetting removal of out-dated standards. It’s not clear as to when students would be expected to learn the new content, particularly in the area of statistics and linear algebra. CCSS says schools retain flexibility in course sequencing, but it appears undefined as to how assessments will be assigned to individual students who are at different stages of math development at any set time in their high school careers. The greater emphasis on application probably disadvantages students with slower cognitive math processors. Such tests are more language dependent and will certainly impact ELL negatively. If instruction is redirected away from textbook based instruction and toward SDAIE friendly computer based pedagogies, a potential exists for at risk groups to indirectly benefit from pedagogical reforms that will result from CCSS.
Student Feedback – A series of student roundtables should be implemented to hear their thoughts regarding these proposed changes. The six sample questions would be a good place to start. These roundtables could be organized by interested teachers, and then share their results in a professional development setting. Participation should begin small in scale and be voluntary, as it may be premature to start a campus wide discussion on a controversial assessment reform that is still a work in progress.
Middle School Preparation Even More Critical - Given the expanded math curriculum, matriculating students that have deficient math skills will offer an even larger challenge than present. In reviewing the eighth grade CCSS, specific standards were identified where a critical need for remediation will likely exist. Presently, a substantial proportion of 8th grade students enter high school without having mastered the skills listed below (not intended to be an exhaustive list).
o Work with radicals and exponents (8.EE, 1. & 2.)
o Solve Linear Equations in One Variable (8.EE, 7.)
o Analyze & solve pairs of simultaneous linear equations (8.EE, 8.)
o Understand congruence and similarity using physical models, transparencies and geometric software. (8.G)
o Investigate patterns of association in bivariate data (8.SP)
I encourage your feedback and comments on my perspectives as well as sharing your views on the subject. Reach me at annelson@ghchs.com .