Last week, Education Week hosted a webinar addressing the mathematics standards that were most challenging for students to master. The webinar identified broad groups of standards in measurement, modeling with mathematics, fractions, and statistics and explained how these concepts build on one another. The presentation illustrated a trajectory in which elementary students who did not master early concepts continued to struggle with more advanced concepts in later grades. For example, students who did not master concepts such as length in elementary school also struggled with line graphs and coordinate grids in middle school.
This analysis prompted Learning List to think about the Common Core mathematics products we’ve reviewed. In particular, we wondered which mathematics standards were least aligned in the products we’ve reviewed. We analyzed our data to identify the CCSSM standards that were not addressed in at least half (50%) of the products for which we’ve verified CCSS alignment.
Our analysis did not identify any standards at grades K-5 for which 50% or more of products were not aligned. Individual products were not aligned to some standards, but no one standard in any grade level was consistently not aligned in 50% or more of the products.
At the middle school level, our analysis identified two standards that 50% or more of products did not address:
- At grade 6, we have reviewed 12 products; 58.3% of these products did not address CSCCM 6.SP.5: Summarize numerical data sets in relation to their context.
- At grade 8, we have reviewed 12 products ; 50% of these products did not address CCSSM 8.G.5: Use formal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles.
At the high school level, we identified four standards for Algebra I and three standards for Algebra II that were not addressed by 50% of products:
- For Algebra I, of the eight products we have reviewed:
- 50% did not address CCSSM A-REI.4: Solve quadratic equations in one variable.
- 50% did not address CCSSM F-IF.7: Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.
- 50% did not address CCSSM F-IF.8: Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.
- 50% did not address CCSSM F-LE.1: Distinguish between functions that can be modeled with linear functions and with exponential functions.
- For Algebra II, of the four products we have reviewed:
- 50% were not aligned to CCSSM A-SSE.1: Interpret expressions that represent quantity in terms of its context.
- 50% were not aligned to CCSSM A-REI.11: Explain why the x-coordinates of the points where the graphs of y=f(x) and y=g(x) intersect are the solutions of the equation f(x)=g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/ or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.
- 50% were not aligned to CCSSM F-IF.7: Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.
The results of our analysis indicate that publishers have greater difficulty meeting the CCSSM in high school algebra courses. If a specific instructional material does not align to 100% of the CCSM standards, Learning List has a key feature, Fill-in-the Gap™, that identifies other products that align to the remaining standards. If needed, this enables educators to use at least two instructional materials that, in the aggregate, would align to 100% of the CCSM standards.
In a subsequent post, we will examine our TEKS data to identify the least aligned mathematics standards in the products we’ve reviewed. We welcome your comments or questions about this topic; please send comment/question to firstname.lastname@example.org.