Not an Easy Discussion

A discussion that must occur in school districts with the advent of the Common Core Learning Standards is how to adhere to Part 100.4d of the State Education Law.

Public school students in grade eight shall have the opportunity to take high school courses in mathematics and in at least one of the following areas: English, social studies, languages other than English, art, music, career and technical education subjects or science courses.

http://www.p12.nysed.gov/part100/pages/1004.html

This means that school districts must address the issue of how to accelerate students without losing any of the rigor or coherence of the Common Core curriculum. For math coursework in many cases this will provide an opportunity for the student to take either Calculus A/B or Calculus B/C in their senior year of High School.

What happened in many instances in the past was that students would take the Algebra 1 course in place of the 8^{th} grade course. Now schools need to consider the impact that this may have due to the fact that the Grade 8 Common Core curriculum contains material that impacts both the Algebra 1 and the Geometry course in high school.

For example, the 8^{th} Grade Functions Standards build the foundation for understanding of linear, quadratic, and exponential functions in Algebra 1. The 8^{th} Grade Geometry Standards build the foundation for understanding irrational numbers& the Pythagorean Theorem in Algebra 1 and Transformations in High School Geometry.

With the advent of the Common Core State Standards, common threads are interwoven throughout the curriculum. These common themes can be seen in the Progression documents, which can be accessed at http://ime.math.arizona.edu/progressions/.

But perhaps the most striking example of coherence in the mathematics curriculum is the intuitive and “hands on” work done in Grade 8 with Congruence & Similarity that form the basis for a more formal treatment of those same concepts in Grade 10 Geometry.

Congruence is no longer defined as geometric figures with the same size and same shape, but rather as a composition of rigid transformations (translations, reflections, and rotations). In Grade 8, students get “hands on” experience with these transformations using transparency paper, among other tools, to physically rotate, move, and reflect different geometric objects both on and off the coordinate plane. This then forms the foundation for more formal work with these concepts in Grade 10 as students use constructions as a basis for these transformations.

Many teachers may argue that the new standards take time to teach effectively and that it is not possible to advance or speed up the process. But if schools are to comply with Part 100.4d, they must at least provide an opportunity for students to compress the middle level content in order to have the opportunity to take Algebra 1 in 8^{th} Grade.

This leaves educators needing to examine options to comply with regulation as well as do what is in the best interests of students.. I think that the Common Core standards are robust in themselves, and teachers need time to focus on the varied nuances within the standards and their application to real world situations. However, since school districts must comply with Part 100, options must be considered to compress the middle school curriculum. To add to this issue, if material from the 7^{th} Grade curriculum is added to the 6^{th} Grade curriculum, for example, care must be taken that all of the 6^{th} Grade Standards are taught prior to the New York State 6^{th} Grade Common Core Exam in April. There could also be an issue with a 6^{th} Grade teacher who might not be certified 7-12, teaching 7^{th} grade material. An end of year assessment might be advisable to ascertain the students’ grasp of the 7^{th} Grade Standards that will be addressed after the April exam.

The issue then becomes, does a school district compress 4 courses into 3 years or do they compress 3 courses into 2 years. Criterion for who should be allowed to accelerate needs to be discussed, as well as on and off ramps for students who need to enter or exit depending on when they mature mathematically or begin to feel overwhelmed.

Another idea for consideration is enhancing the curriculum rather than accelerating it. This approach would not solve the issue of compliance with Part 100, but it could address the issue of giving a student the ability to take a Calculus course in their senior year.

As mentioned previously, the Common Core Standards are robust in and of themselves. These Standards coupled with the (+) Standards in the High School curriculum and some other additions to the Algebra 2 curriculum could enable students to take a Calculus A/B course in their senior year, thus skipping Pre-Calculus. The (+) Standard are ones which are suggested, but are not evaluated on state exams. This might be a viable option as part of what used to be taught in Pre- Calculus is now in the Common Core Algebra 2 curriculum.

As a former High School Mathematics teacher, I realize the importance of having a quality honors program in mathematics that students can access at different points in their academic career. Students should be challenged no matter what course they are taking. With all the concern about the adoption of the Common Core Learning Standards, not enough attention was placed on students at the high and low end of the learning spectrum.

The reason that I wanted to “put this out there”, is that I think this discussion is necessary and, at the same time, not easy. All stakeholders should be involved. That means that high school teachers will have to sit down with middle school teachers, guidance and administration to work out an option that benefits all students in their district. This will not be easy. Combining topics in Middle School will mean more prep time and collaboration between grade level teachers. Enhancing the High School curriculum so that students can skip Pre-Calculus and take Calculus A/B in senior year will mean present day Pre-Calculus teachers may lose some sections.

And then there is another question to ask. Is it really that important for students to go faster through middle school standards just so they can take Calculus in high school? My own feeling is that students should bore deeper into the Standards at each grade level and develop better project based learning skills that apply these standards to real life issues. Perhaps the Common Core Pre-Calculus course with its emphasis on Complex Numbers, Transformations, Vectors, Matrices, Trigonometry, and Probability and Statistics is more advisable.

Whatever route school districts take, this is a discussion that must take place, and one that will have far reaching consequences in the future.

What do you think?

Jack McLoughlin

jmcloughlin@ocmboces.org

OCMBOCES Network Team

Math Consultant