Standards are expectations. They are statements on skills. For example, we expect students to know 2+2=4 and why. Decisions about standards are made at the state level, and they define for teachers and all stakeholders what students should know and be able to do by the end of the year.
Curriculum is the plan/program created or adopted by local school districts to teach students to learn the standards (e.g. 2+2=4). Curriculum includes many resources: activities, lessons, units, assessments, and may include publisher textbooks.
Standards are the end. Curriculum is the means.
In 2010, the California Department of Education adopted the CA Common Core Standards for K-12 mathematics. These math standards place a stronger emphasis on a balanced between conceptual understanding, application, and procedural fluency and skill. Our math department has mapped out the essential standards that need to be taught at each grade level and aligned them to resources to develop a curriculum to help students learn these standards.
Some of these resources have been purchased by our district, while some are free, on-line resources. Our goal is to create a viable and guaranteed curriculum. Viable, meaning the standards that need to be learned can be taught in the time given. Guaranteed, meaning all teachers at the same grade level will cover the same essential standards and incorporate common assessments. All students have standards-aligned instructional materials to use in class and to take home.
However, this is not a lock step program, meaning it is up to each individual teacher to identify the resources and a window of time to personalize the learning of the essential standards for THEIR students EACH year; it is not a “must teach standard ‘x’ on a specific date.”
The vehicle to teach the standards is Cognitively Guided Instruction (CGI) in grades K-5 and Balanced Mathematics in grades 6-12. CGI/Balanced Mathematics is based on decades of research in how children learn mathematics; a compilation of studies can be found here. The “balance” in Balanced Mathematics aims for an equal amount of time to be spent on conceptual understanding, application, and procedural and skill fluency. The former 1997 California Standards that we have been operating under relied heavily on procedural and skill fluency.
In grades K-5, teams of teacher have taken the standards for their grade level and aligned them to a variety of resources for teachers to use. These resources include, but are limited to: Eureka Math, Engage New York, Georgia Units, word problems, number talks, and math wall cards. During the 2015-16 school year, the MBUSD Math Committee went through a textbook adoption. The textbooks selected, Everyday Math and Go Math!, will be used an additional resource for grade K-5. However, teachers are responsible for teacher students the state standards, not a textbook cover to cover.
In grades, 6-12, teacher have taken the new standards and aligned them to resources such as UC Irvine Math Project Units, Illustrative Mathematics (online program developed by one of the Common Core authors, Eureka Math, and Maneuvering the Middle.
The former 1997 California Content Standards were the sole set of standards describing the expectations of what students must learn by course and grade level; however, the California Common Core Standards have identified not only what needs to be learned (California Common Core Standards for Content), but also how mathematics should be learned through a set of eight K-12 standards of productive mathematical skills and practices (California Common Core Standards for Mathematical Practice).
Assessments are moving away from the scantron/multiple choice options that we have seen for decades. Many of you may have seen the parody “I Choose C,” that exaggerates this multiple-choice phenomenon, thus de-emphasizing true critical thinking. The new assessments, both Smarter Balanced Assessment Consortium (SBAC) and the formative assessments teachers have begun implementing, aim to address the four Depth of Knowledge Levels (note: there are Depth of Knowledge matrices for both Math/Science and English Language Arts). Due to the utilization of computers, rather than students filling out a scantron, assessments have become more sophisticated in that the SBAC is computer adaptive and can engage students in a wider variance of question types aimed to uncover higher levels of rigor and critical thinking. Here is a link to the SBAC question types.
Overall, homework will consist of fewer problems, but examined at a deeper level through multiple solutions or “proving” the answer through another solution, which means homework assignments like page 67 odd should go away with time. Research has found that students build greater connections and understanding when they solve several problems in a couple different ways than a sheet of problems solving them all the same way. Students should not be marked down for solving a problem a different way than what was discussed in class as we know that there are a variety of ways to solve equations.
The best way to help is to avoid telling him/her how to solve a problem. This is very different than what we are inclined to do; however, the Standards for Mathematical Practice (SMP) aim to develop your student as a problem solver. Traits of being a problem solver are persistence, modeling with mathematics, applying strategies already known to novel situations, and developing plans to approach problems. It is recommended that parents embrace this notion of productive struggle through the use of questioning. Here is a great resource to use when questioning your student at home. Note, the term is productive struggle, not overt frustration. It is okay to break down a problem to further help your child, but try and steer clear of any “tricks” we learned as students as they typically don’t teach the math behind the math. The overall goal is to get students to the algorithm; however, to build conceptual understanding students need to make their own connections to prior knowledge, multiple concepts, and strategies for problem solving. Most likely these initial strategies will not look like the traditional algorithm, but know the goal is to move them there with a solid conceptual foundation. Here is a video of Phil Daro, one of the contributors to the Common Core, speaking about math tricks. Additional resources can found at the bottom of this page.
How often do you find yourself solving a single problem type? For most people, rarely. Problems in college and career do not fit neatly into a box, but rather consist of complex situations where we must persevere and draw from a variety of problem solving skills. The new standards take into account that our world is changing, that the future jobs of our students may not even exist, but having rich toolbox of problem solving strategies, combined with grit, will be of great advantage. Here is a compilation of studies in the area of CGI mathematics.