K-12 Mathematics Program Review Frequently Asked Questions

• Kindergarten—Count on Math (Gryphon House Book), Houghton Mifflin Mathematics, Fall in Math & Science (Project Aims)
• Grade 1—Used Numbers (Susan Jo Russell & Antonia Stone), basic facts worksheets
• Grade 2—Scott Foresman Addison Wesley Mathematics for problem solving practice
• Grade 3—Wizards (teacher created program incorporating all standards)
• Grade 4—Harcourt Brace Mathematics Today for skills practice
• Grade 5—Teacher created curriculum and an older version of Addison Wesley.

Math coaching offers a systematic way for schools and districts to focus on the teaching and learning of mathematics. Systems have to be ready for change in order for math coaching to be effective. In Amherst we are poised for these changes—we want these changes. Coaches keep the focus on mathematics and cultivate a culture of inquiry among all learners. Coaching means there will be a concerted effort toward strengthening mathematics practice and mathematics learning for students and adults.

The overall goal of a math coach is to improve the teaching and learning of mathematics in schools. Coaches are the in-house professional developers; they are the people who press for understanding, rigor, engagement, learning—they are the teachers of teachers. They work with teachers in different contexts: in the classroom, at grade level meetings, and at other after- or during-school contexts. There are three important objectives math coaches keep in mind as they provide support for teachers:

• Develop a strong understanding of the content they teach;
• Focus on student ideas; and
• Make teaching more public.

Learning more about the important mathematical ideas in the elementary curriculum is exciting and empowering. As teachers learn more, their energy for teaching increases. Coaches can teach “content” based courses, which is often done outside of the school day. Content-based courses focus on the underpinnings of the important mathematics in elementary school, often connecting and seeing the interrelationship between equations, story contexts and representations. If this sounds different from your experience in elementary school, it is. Much has been learned about what a teacher needs to know in order to teach well. Math coaches do much of this work.

Learning can also happen during the school day. Coaches meet with teachers before they teach a lesson—they do the math of the lesson together, review students’ assessments and/or classroom work, and plan together for the next steps to increase student understanding and improve outcomes. These meetings are opportunities for teachers to be intellectually engaged in the ideas of their students and to do it with a knowledgeable practitioner. 

Coaches also facilitate visits to classrooms and conversations between teachers, enabling them to learn from and with one another. During these visits, all teachers engage in a learning culture that promotes public discussion of teaching dilemmas, challenges and successes. The conversations are designed very specifically with district, school, and individual math goals for student achievement and teacher learning as a guide. Opening the doors of classrooms and making our practice more public is an important piece of a coach’s work. 

Graduate courses and modules in mathematics content will be offered to teachers through collaboration with DESE, DASC, Five Colleges and online courses. These courses and modules will be offered during the summer and after school. In-depth and ongoing professional development in instructional program delivery and training in the Practice Standards of the Common Core will be provided for  teachers during either summer courses, building-based staff in-service, release day sessions, after school courses, and/or curriculum days. Financial support will be obtained to support teachers in grades K-8 to take graduate level courses in math.

If we are to expect a level of proficiency with mathematics content, we will need to provide professional development to all teachers. As is our current practice, we will sit with the leadership of the teachers union at the local and regional levels and complete a needs assessment to identify the differentiated needs of our teachers. Implications for budget will be determined through collaboration with the business and human resources offices. Finally, we will use a formal system to identify teachers who will attend Learning Labs and model classrooms and will provide release time for these teachers to observe teaching and learning in math.

As above, we will partner with the leadership of the teachers union, human resources, and the business office to deliver necessary professional development in mathematics.

The decision to make a full curriculum change requires a thoughtful and careful textbook review process. Responsible, transparent and critical decision-making around a textbook adoption must be research-based and aligned with the Common Core Standards. In addition, any math textbook selected needs to address the grade level content standards and the standards for mathematical practice in the Massachusetts Curriculum Framework for Mathematics (January 2011). Sufficient time is needed to provide initial and on-going, differentiated teacher support to begin and support implementation.

Our current math program in grades K-5, Investigations in Number, Data, and Space (second edition) consists of 60 minutes of math instruction daily in grades 1-5. Due to its AYP status, Crocker Farm School is required to provide 70 minutes of math instruction daily. In Kindergarten, the lessons are between 30 and 45 minutes long.   In addition, there is another daily ten minute math session in grades K-5 called Classroom Routines (K-3), or Ten Minute Math (3-5)which occurs outside the regular math lesson.   The grade 6 program, Impact Course 1, consists of daily lessons that are approximately 45-60 minutes long (grade 6 teachers are required to teach math for a full hour). Some Amherst teachers spend more than the required time on math while a few spend less than the required time. It is anticipated that the current 60-70 minutes of math will be the minimum requirement for FY 12. 

Educational factors, rather than social reasons, should drive family decisions when it comes to choosing math courses at the high school. ARHS has excellent teachers in both pathways. There is no advantage of one program over another with respect to teacher quality.  The differences between the two programs can be viewed in terms of their strengths relative to meeting the goals of NCTM and Common Core Standards for Mathematics as reflected in the State Mathematics Frameworks. Neither program is perfect. Parents and students should consider the features of each and decide which they value most.

IMP is especially strong in the way it meets the process or mathematical practice standards. These include problem-solving, reasoning, communication and connecting mathematical ideas especially through different representations. Our traditional program is less strong on process but stronger on developing skills and in the breadth of traditional topics covered. It is important to know that we are working to deliver balanced instruction (conceptual understandings, skills practice, and problem-solving) in both pathways. Here are some ways in which IMP and the traditional program differ significantly: 

• Problems of the Week (POWs).  These are extended, long-term problems for which the method of solution is not immediately apparent. They require students to experiment to find an entry point to the problem and persist, sometimes through missteps and unsuccessful attempts. Students develop problem solving strategies by experimenting and by writing about their process. Students develop their mathematical reasoning by justifying their solutions in writing as well. Over the course of 4 years, students will work 40-50 POWs, so over time POWs are very powerful in helping students develop mathematical habits of mind. Our traditional program does not have this feature.

• IMP Unit Problems. Most units in IMP revolve around a big central problem which students do not initially have the knowledge and experience to solve. Over the course of 4-5 weeks, students develop the concepts and skills needed to solve the problem. Students, therefore, see their daily work as purposeful. We don’t hear students say, “When will I ever need this?” The unit problems also tie together mathematical strands like algebra, geometry, trigonometry and statistics, addressing the process goal of connections. Unit problems are deep enough to challenge the most experienced students and concrete enough for all students to develop mathematical understanding. Topics in our traditional program are not organized in this way. While ideas and skills tend to build, the curriculum proceeds through a list of topics with less emphasis on connections and application.

• Content. In general, IMP covers all the traditional strands of high school algebra, geometry, algebra 2, trigonometry and pre-calculus. Within these traditional content strands, IMP covers somewhat fewer specific topics than our traditional program. The trade off is that IMP has extensive development of probability, statistics and discrete mathematics. Our traditional program has little treatment of probability, statistics and discrete math topics. Outlines of topics, concepts, and skills for all four years of IMP can be found at the publisher’s website: http://www.keypress.com/x4681.xml.

• Integrated vs. Separate Courses. In IMP, students develop ideas and skills in all areas (algebra, geometry, trigonometry, probability, statistics, etc.) in all four years of the program. Different units have different emphases, but connections between mathematical ideas are also emphasized within units. This is part of the deliberate effort to meet the process standard of connection and representations. In our traditional program there is development of connections but major strands are divided into separate courses (Algebra 1, Geometry, etc.)

• Heterogeneous vs. Tracked Classes. In IMP, honors and college prep students work together in the same classroom. In our traditional program, honors and college prep students are tracked into different classes. There is a philosophical and pragmatic issue here. We believe that a public school should not reinforce the many divisions that exist in the society at large. Tracking tends to do just that. Some people believe strongly that we should work actively to counter such divisions. On the other hand, one cannot simply throw all students together on principle and hope it all works out. IMP was specifically designed and tested to challenge students with diverse mathematical backgrounds in a heterogeneous classroom.   In IMP, all students are working to attain a set of high expectations.   Honors students are expected to meet those expectations at a very rigorous level while college prep students may progress and develop at somewhat different rates. 

• Curriculum Coordinator (1.0 FTE)           $55,000
• Increase in Math Coaches (0.2 FTE)       $10,000
• Professional Development                        $30,000
• Supplemental Materials                            TBD

The final coaching model to be used going into the future is still under consideration. At most, the model would require additional funds for FY12 as follows:

• Additional for Amherst (3.0 FTE)            $265,000
• Additional for Pelham (0.5 FTE) $ 25,000
• Additional for ARMS (1.0 FTE) $ 55,000

These funds are NOT included in the FY12 budget. The districts intend to seek grant or corporate funding to support this model of coaching.

Finally, if the decision is made to replace elementary mathematics textbooks, the cost will be approximately $150,000. This expense will be included in the FY13 budget.

Dr. Chen strongly recommended the importance of building “an embedded self-sustained mathematics learning community” as a form of professional development that brings together teachers of mathematics at many grade levels to support the learning of mathematics content knowledge and strengthen pedagogical content knowledge. Math coaches both in and out of classroom instruction will facilitate effective learning communities. Math coaches provide the important classroom implementation follow-up to content coursework. 

Dr. Amy Wolpin’s research (2006) examining the effectiveness of math coaches as teacher leaders found that coaching promotes collaborative, job-embedded professional development to improve students’ mathematics achievement. In addition, math coaches can directly address the pervasiveness of the affective domain that impacts teachers even as they choose to improve their practice.

Effective and comprehensive implementation of curriculum requires the on-going support of teacher learning to promote student learning (S. Russell, 1998).

The textbooks that were selected for review are those used most often by comparison/benchmark districts nationally and in Massachusetts.

We offer Math 8, Algebra H, and Geometry H to students in 8th grade.  Additionally, some students take a pull-out math class if that is required by their IEP.  Math 8 includes a significant amount of Algebra I material, but not the entire course.  We also teach other non-algebra strands of mathematics.  Students who take Math 8 move on to either regular or honors level Algebra or IMP at the high school, although a few take pre-algebra courses if needed.

If we offered an eighth grade Algebra course, it would be for the students who take Algebra H in ninth grade in our current course sequence. Many students in Math 8 have not established the foundation necessary to be ready for Algebra.  If they took Algebra in 8^th grade, this would prepare them for a regular level mathematics track at the High School.  Students in the regular track are not prepared for Calculus and; therefore, would not be able to take it as seniors.  It has been the district's stance that it is better for students to take honors level curriculum than to be a year further in the math sequence upon graduation.

Yes, the U.S. standard algorithm is in the curriculum. There is an expectation in the elementary curriculum that students use efficient, accurate algorithms. “When they are firmly grounded in understanding the operation and solving problems accurately, efficiently, and flexibly, they study and compare algorithms, including the U.S. traditional algorithms for addition, subtraction, multiplication in order to learn about the mathematical relationships underlying them. In particular, students’ algorithms for solving addition and multiplication problems are usually quite similar to the historically taught algorithms in the United States; with a solid foundation in more transparent methods, students are ready to learn how the shorthand notation of these algorithms relates to the procedures they are carrying out but notating differently” (Russell, Susan J. Research: Computational Algorithms and Procedures 2009). By 5^th grade students will have been exposed to all the U.S. standard algorithms. Visit this link to read the entire article referenced above: