ARHS Math Curriculum Review FAQ
- ARHS has been using IMP for years, why don’t we just compare our own internal results to see which is better, IMP courses or “Traditional” courses?
- A valid direct comparison of results cannot be made between the IMP courses and the traditional courses within ARHS. The main reason we cannot do this is because students were not randomly assigned to the courses. Enrolling in IMP or traditional courses is a choice and as such does not result in a random sample of representative students in each course sequence. Students have chosen to take IMP or traditional courses for many reasons; therefore it would not be appropriate to analyze these cohorts as representing Amherst students on the whole.
- The fact that the cohort of students who take IMP courses does not mirror the cohort of students who take Traditional courses is evident by multiple indicators, for example:
- (Between 2005 and 2011) The cohort of students in IMP courses is weighted heavily towards students who did not take Algebra in 8th grade, by a ratio of about 3 to 1. The cohort of students in traditional courses is approximately evenly split between students who took Algebra in 8th grade and those that did not. In other words, the traditional courses are usually split 50/50 between students from the regular 8th grade course and the advanced 8th grade course. The IMP classes typically have 3 times as many students from the regular 8th grade course than students from the advanced 8th grade classes. Additionally, under the old course structure and the pre-2011 standards, very high performing students may have taken Geometry in 8th grade, in all cases these students went into the traditional courses at ARHS.
- The 7th and 8th Grade MCAS performance of students entering the IMP or Traditional tracks are not similar. For example, the vast majority of students who scored advanced on the MCAS in 7th or 8th grade enrolled in Traditional courses at ARHS and therefore substantiated a larger portion of students in those classes. Students in IMP classes are more likely to have scored “Proficient” or “Needs Improvement” in 7th or 8th grade on the MCAS.
- Considering that IMP is one of the programs under review what can we see in our own internal data?
- In our current model, taking Calculus in 12th grade requires students to take a prerequisite class in 11th grade, IMP 4 or Pre-Calculus. Students who meet this prerequisite represent a cohort that is generally high performing; they likely have done well in Honors courses since 8th grade. Among this cohort, students have successfully gone from IMP 4 into Calculus AP courses.
- The course grades of students coming from IMP 4 into Calculus mirror those of students from the traditional sequence.
- Typically, students from the IMP sequence perform above average on the SAT.
- About 90% of students from IMP classes are proficient or Advanced on the 10th grade MCAS.
- What types of colleges were contacted regarding admissions?
- We spoke with state and private colleges in and outside of Massachusetts, including schools which traditionally specialize in the STEM fields. There is consensus among the colleges contacted that both traditional and integrated course sequences are acceptable. There were no reports that an integrated course sequences has a negative effect on college acceptance. All colleges report having guidelines for interpreting transcripts that include integrated courses. Colleges primarily rely on the program of studies if any additional information is needed. It is worth noting that admissions departments are reviewing transcripts from around the world, therefore they are prepared for a wide range of variability.
- How will the suggested course sequences be impacted by a potential schedule change at ARHS?
- Currently the Draft Math Course Sequences contain 1st trimester electives for students interested in moving from the College Prep sequence to the Honors sequence. This allows students to take an Honors course for terms 2 and 3. If ARHS were to move to a different schedule these electives would necessarily change. Given a block schedule the elective would likely consist of a 1st term course. Given a semester model the elective would likely become a course running parallel to the student’s regular math course.
- Why are electives suggested between courses?
- We are suggesting the creation of electives between math courses to allow for more flexibility between College Prep and Honors courses. These electives are not a required part of the course sequence, but serve as an option for a student who would like to move into the Honors sequence after 8th grade. Also, we are suggesting an elective to help students transition from 8th grade to 9th grade as needed.
- Why isn’t there a transition elective later than 10th grade?
- The elective exists in 9th and 10th grades to allow students to transition between CP and Honors courses. The difference between the CP course and Honors course in 11th grade would be too large to cover in a one trimester course.
- In what ways will writing be a part of a typical math class at ARHS?
- The 2011 Massachusetts Math Frameworks are written to reflect 6 guiding principles. The sixth principle is Literacy Across the Content Areas:
Reading, writing, and communication skills are necessary elements of learning and engaging in mathematics, as well as in other content areas. Supporting the development of students’ literacy skills will allow them to deepen their understanding of mathematics concepts and help them to determine the meanings of symbols, key terms, and mathematics phrases, as well as to develop reasoning skills that apply across the disciplines. In reading, teachers should consistently support students’ ability to gain and deepen understanding of concepts from written material by helping them acquire comprehension skills and strategies, as well as specialized vocabulary and symbols. Mathematics classrooms should make use of a variety of text materials and formats, including textbooks, math journals, contextual math problems, and data presented in a variety of media.
In writing, teachers should consistently support students’ ability to reason and achieve deeper understanding of concepts, and to express their understanding in a focused, precise, and convincing manner. Mathematics classrooms should incorporate a variety of written assignments ranging from math journals to formal written proofs.
In speaking and listening, teachers should provide students with opportunities for mathematical discourse using precise language to convey ideas, communicate solutions, and support arguments. (See Standard for Mathematical Practice 6: Attend to precision.)
- Specifically the 2011 Massachusetts ELA and Writing Frameworks outline writing anchor standards that should inform the work of math teachers. For example
- 1. Write arguments to support claims in an analysis of substantive topics or texts, using valid reasoning and relevant and sufficient evidence.
- 4. Produce clear and coherent writing in which the development, organization, and style are appropriate to task, purpose, and audience.
- 10. Write routinely over extended time frames (time for research, reflection, and revision) and shorter time frames (a single sitting or a day or two) for a range of tasks, purposes, and audiences.
- Do the 2011 Massachusetts Math Frameworks dictate specific teaching methods?
- The 2011 Massachusetts Math Frameworks are written to reflect 6 guiding principles. The first principle is Learning:
Mathematical ideas should be explored in ways that stimulate curiosity, create enjoyment of mathematics, and develop depth of understanding.
Students need to understand mathematics deeply and use it effectively. The Standards for Mathematical Practice describe ways in which students increasingly engage with the subject matter as they grow in mathematical maturity and expertise through the elementary, middle, and high school years.
To achieve mathematical understanding, students should have a balance of mathematical procedures and conceptual understanding. Students should be actively engaged in doing meaningful mathematics, discussing mathematical ideas, and applying mathematics in interesting, thought-provoking situations. Student understanding is further developed through ongoing reflection about cognitively demanding and worthwhile tasks.
Tasks should be designed to challenge students in multiple ways. Short- and long-term investigations that connect procedures and skills with conceptual understanding are integral components of an effective mathematics program. Activities should build upon curiosity and prior knowledge, and enable students to solve progressively deeper, broader, and more sophisticated problems. (See Standard for Mathematical Practice 1: Make sense of problems and persevere in solving them.) Mathematical tasks reflecting sound and significant mathematics should generate active classroom talk, promote the development of conjectures, and lead to an understanding of the necessity for mathematical reasoning. (See Standard for Mathematical Practice 2: Reason abstractly and quantitatively.)
- The 2011 Massachusetts Math Frameworks also dictate 8 Standards for Mathematical Practice. Teachers are expected to teach and assess these practices. MCAS will be updated and/or we will move to the PARCC assessment, in either case these practices will be assessed. The Standards for Math Practice describe the skills students must use to engage with and learn mathematics. Specifically, Standard 3: Construct viable arguments and critique the reasoning of others, refers to expected observable student behaviors in the classroom.Mathematically proficient students understand and use stated assumptions, definitions, and previously established results in constructing arguments. They make conjectures and build a logical progression of statements to explore the truth of their conjectures. They are able to analyze situations by breaking them into cases, and can recognize and use counterexamples. They justify their conclusions, communicate them to others, and respond to the arguments of others. They reason inductively about data, making plausible arguments that take into account the context from which the data arose. Mathematically proficient students are also able to compare the effectiveness of two plausible arguments, distinguish correct logic or reasoning from that which is flawed, and—if there is a flaw in an argument—explain what it is. Elementary students can construct arguments using concrete referents such as objects, drawings, diagrams, and actions. Such arguments can make sense and be correct, even though they are not generalized or made formal until later grades. Later, students learn to determine domains to which an argument applies. Students at all grades can listen or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments
- In accordance with the High School Publishers’ Criteria for the Common Core State Standards for Mathematics we expect our math classes to be rigorous as defined in: http://www.corestandards.org/assets/Math_Publishers_Criteria_HS_Spring%202013_FINAL.pdf
Therefore, it is the expectation that our math classes balance procedural fluency, conceptual understanding, and application of math. Balancing these three aspects of learning requires teachers to engage students using multiple methods. Either extreme of strict lecture versus exclusive use of exploration would make a balance classroom experience difficult.
- How do the potential changes in the math courses connect with the ARHS vision?
- Schools everywhere aspire to ensure that their curricula in all subjects are 'standards-based'. Standards describe what the professional community of a particular discipline has determined all students should know and be able to do. The work of ARHS and all schools isn't just to admire these standards. Instead, the work is to operationalize them. To ensure that all math curriculum and instruction is aligned with them and that they actually drive the daily work of every math classroom. By doing so, all ARHS students will have access to the knowledge and skills that best correlate with the preparation for the demands of the 21st century. This is true for both academic and career pursuits. Providing all students with access to these highly valued knowledge and skills is a cornerstone of ARHS's commitment to enhance the life chances of all students.
- When did the review process begin?
- Over the last two years the ARHS Math department has been working to update math courses to align with the 2011 Massachusetts Mathematics Frameworks and reviewing curricula. Here are some highlights of the work to date:
- 5 day norming departmental understanding of the Standards for Mathematical Practice
- Department went through design process to create a program review criteria, based on the review criteria used ARMS.
- Department spent one full day reviewing each of the following curricula
- College Preparatory Math (CPM) – with New England Regional Coordinator for Professional Development
- Center for Mathematics Education Project (CME) – with Sales Representative and ARHS teacher
- Core-Plus – with program expert and professor from local university
- Interactive Mathematics Program (IMP) – with ARHS teachers
- Another program was reviewed for part of day, Carnegie Learning – with ARHS teachers
- Department members integrated materials from the above curricula into their lessons to gain insight into the use of the materials and share with the department
- Three ARHS teachers participated in professional development at a nearby school using College Preparatory Math and reported back to the department
- Three ARHS teachers visited a local school using the Core-Plus materials.
- Will Honors courses still exist?
- Yes, there will Honors sections and College Prep math sections at ARHS regardless of the curriculum chosen. Please see this preliminary course sequence.
- Will my student be able to take Calculus at ARHS?
- Yes, all curricula under consideration include Pre-Calculus content to prepare students for Calculus. The expected Honors course sequence would prepare students for Calculus in 12th grade.
- What students will this change effect?
- Current 8th grade students and younger will be effected by the change. Also, student currently enrolled in Algebra or IMP 1 at ARHS will follow the updated course sequence.
- What are “integrated” and “traditional” curricula or course sequence?
- The difference between an “integrated” and “traditional” curriculum has to do with the order the content is covered. A “traditional” approach to curriculum means courses are designed to contain Algebra topics or geometry topics. Courses in this sequence are typically named, Algebra 1, Geometry, and Algebra 2. In an “integrated” curriculum the courses will cover algebra along with geometry topics, for example. This is the typical model outside of the United States. Course may have names like “Math 9” for 9th grade and so forth. Students learn the same content as they would in Algebra 1, Geometry, and Algebra 2 but not in that particular order. It is important to know that districts are expected to include statistics in all classes, as such even in the “traditional” model there is some elements of integration.
- Both models:
- Are acceptable to meet the 2011 Massachusetts Math Frameworks.
- Can prepare students for AP Calculus in the High School
- Will prepare students for standardized tests (MCAS, PARCC, SAT, etc)
- What criteria is the ARHS math department using during this review process?
- The criteria the ARHS math department is using for the math curriculum review is focused on three main areas; Rigor, Standards for Mathematical Practice, and Differentiation. These areas go beyond the basic criteria of standards alignment and a research base of positive student impact. These three areas are based guidelines from the Common Core Standards, the 2011 Massachusetts Mathematics Frameworks, and teaching best practices. Click here for more information about these criteria.
- How were these curricula chosen for review?
- The curricula under review were chosen based on:
- Use in other successful school districts
- Research base of positive student impact
- Alignment with the 2011 Massachusetts Frameworks