Purpose: The purpose of this document is to provide answers to the questions that have been asked over the course of selecting and adopting the Math Expressions for all elementary schools in the Boulder Valley School District. Statement: We believe that adopting one balanced program as the core instructional materials for all elementary school mathematics instruction will provide a firm and consistent foundation, with common language and strategies, for all of our students. Best instructional practices are supported by the best instructional materials. Rationale: The Math Expressions materials were found to be the most accurately aligned to the new standards at the precise grade level indicated in the standards documents, without excessive extraneous materials. The materials include not only the content standards but the Standards for Mathematical Practices 1 as well. In particular, the materials embrace the intent of the new standards - rigor through deeper understanding and problem-solving. This program supports many of the instructional best practices already in place in BVSD, including classroom discourse (or math talks ) in each lesson, modeling and developing mental math skills. Additionally, the program supplies students, teachers and parents with robust and appropriate online and print support materials. Overall, this is a balanced, coherent and rigorous program. Frequently Asked Questions: These questions are answered with a combination of research, feedback from teachers, committee and community members, and statements from district leadership or the publisher. I. What about the program did the committee and community like? (Statements are from public review and committee feedback. Redundancies are excluded.) Standards Alignment This program aligns with the common core and the spiral is nice to have so we know the student will revisit the content at a higher level later I can tell that Math Expressions was written to match the Common Core topics. It has the concept of fewer down. It does follow a spiral concept and it isn't as overwhelming as Everyday Math. Matches common core better than other programs. This program provides a basic instructional sequence for teaching the standards. The materials seem easy to follow and cover exactly what is in the standards so teachers/the district would not need to adjust instruction or fill in gaps. Expanded amount of time on patterning. Strong number sense No extraneous material beyond the CCSS which is good for most K-5 teachers. Systematic and explicit. Consistent representations across grade levels. Fact fluency up front. Connection to algebra Goes beyond CCSS 4 th grade multi-digit multiplication is taught exceptionally well
Student Engagement There are many games and activities. Creates a learning community. Hands-on approach Inquiry based and kids engaged Problem-solving and conceptual understanding Primary lessons very engaging and kids are way ahead Math Expression has students explain their answers, which is useful when doing the TCAP. Units go deep. Puzzled Penguin makes students think and express their thoughts. Quality Instructional Design Math talks throughout Multiple ways to think and solve problems Has been developed, revised and field tested (need to select a series of this nature) has shown success in St. Vrain and Brighton. Teacher and district feedback was very positive. Math (which seems to try to do it all). Linear, organized approach; Excellent teacher's guide; Lessons taught sequentially with opportunities for review; Hard cover student text available children to actually learn that unit. Rigor Positive feedback from St. Vrain Homework practice and remembering Layout easy to follow This program is laid out in a user friendly style. Math Expressions is very easy to read and simple to get through. Organized by big ideas, math talk and drawings. Resources for multiple assessments -- e.g. formative, quick checks, fluency checks, on-line summatives. I like the BIG IDEA vocab I like the multiple strategies model I like the more in-depth instruction, rather than spiraling as in Everyday I love the inquiry-based model and use of constructivist dialogues. I enjoy the use and fluency of multiple strategies, waiting to introduce the standard algorithm model until 4th and 5th grades. Inquiry based Uses multiple strategies guiding towards algorithms 100 lessons of the year offers the opportunity to spend more time when needed. There are metric only exercises. Only using one unit at a time allows Focus on pictorial models with a progression to the algorithm Good for building consistent strategies for number sense Easier for new teachers to use Spiral review in homework Good problem solving base throughout Bridges concrete to abstract My staff loved the math talk aspect Based on high level research from Karen Fuson
Organization of materials with learning progression and easily accessed differentiated instruction It has a component for differentiated instruction. RTI recommendations provided in Tier 1,2,3 books There is homework that connects to each lesson Supports all students learning which makes the homework correlate to the lesson effectively. The objectives and goals are defined as well as when to teach on the white board or have students practice. There are hands-on activities and many practice pages. Technology Offers specific activities for intervention, on level and challenge work. Student handbook with lesson modifications/accommodat ions There are good technology resources. instructional online lesson designs. Math Expression has some very neat and clean Online resources were fun and engaging for kids. Language Support Supports new CELPs by WIDA (Reading, Writing, Listening, Speaking) with activities that require students to share their thinking with a partner, small group or whole group during the summarization part of each Investigation (activity). (Speaking/ Listening) Students are often required to create posters and present their solutions (Speaking). And a list of writing prompts is included after each investigation so that students have the opportunity to express their understanding through writing.(writing) Language support in Glossaries Creates more conversations led by students in the classroom. The book seems easy to read and follow. There are math writing prompts for each lesson which would incorporate writing into the math lessons. There are accommodations for ELL students in each lesson. It has trade literature books with math connections that come with the program. I like the ELL focus and use of more numerical ways of representing thinking strategies. Available in Spanish. Has supports for Ells Good integration of Spanish language materials. This program seems very simple and easy to follow for ELL students.
Parent Support Updated parent support/student online resources Student homework help is available online II. What research supports this style of learning and instruction? How the Brain Learns Math by David A. Sousa: Seems easy to follow Provides letters in Spanish to parents. The goal of learning is not just to acquire knowledge but to be able to use that knowledge in a variety of different settings that students see as relevant. To do this, students need a deeper understanding of the concepts involved in learning. (pg. 55) Beneath the Tip of the Iceberg: Using Representations to Support Student Understanding., by David Webb, Nina Boswinkel and Truss Drekker. (pg. 111). students need to experience a broad range of mathematical models to make sense of formal mathematical representations (i.e., the tip of the iceberg.) Teaching Children who Struggle with Mathematics by Helene J. Sherman, Chapter 1, pg. 3. Mathematics instruction must provide many opportunities for concept building, relevant challenging questions, problem solving, reasoning, and connections within the curriculum and real-world situations. Students who are taught in a way that relies too heavily on rote memorization isolated from meaning have difficulty recognizing and retaining math concepts and generalizations. Teaching Children who Struggle with Mathematics by Helene J. Sherman, Chapter 9, pg. 210. Group efforts can be less threatening to students than working individually. Problem solving ability is enhanced when students share opportunities to solve problems themselves and see problems being solved. (NRC, 2001, p. 420). Classroom Discussions Using math talk to help students learn by Suzanne H. Chapin, Chapter 1, pages 6-7. Classroom dialogue may provide direct access to ideas, relationships among those ideas, strategies, procedures, facts, mathematical history, and more. Classroom dialogue also supports student learning indirectly through the building of a social environment a community-- that encourages learning.
III. I have heard that Math Expressions will not be rigorous enough for my child. Is this true? Jennifer Barr, the Coordinator for Advanced Learning Services, and I agree that curriculum materials are resources for teachers and are not intended to provide all of the unique learning opportunities that diverse student needs demand. Skilled instructors must assess learners' readiness, interests and learning styles and then adjust the content, process, product and learning environment to meet students where they are and take them further. In the BVSD, we do not have a different curriculum for gifted learners. We expect general educators to respond to the needs of gifted learners by adjusting depth, pace and complexity. The committee felt that Math Expressions offered resources to facilitate the adjustment of instruction for the needs of gifted learners. Among other things, Math Expressions provides differentiated instruction labeled "Intervention", "On Level" and "Challenge", differentiated writing prompts and formative assessment for each lesson. Additionally the integration of the Standards for Mathematical Practice not only meets requirements for alignment to the standards, but also provides depth and rigor. There is no one perfect program, but after thoroughly examining six programs, the committee overwhelming selected Math Expressions as the one that was best aligned to the new standards, offered the best instructional support for students and provided the structure and consistency that our district needs. The feedback from St. Vrain teachers provided appropriate feedback about rigor, flexibility and results. IV. How will a program like this benefit all of our population? Math Expressions is a rich program that fully incorporates the Standards for Mathematical Practice and benefits all students with hands-on, real-life situations from which they can make sense and connect to the concept being taught. The quantity and richness of the instructional materials for TAG, ELL, struggling readers and every other student was prominent in the considerations of all of the materials. The committee considered these concerns in numerous places throughout the evaluation and it factored into a major part of our discussions on days three, four and five of the committee process. In fact, the process was extended by a day to allow committee members to further delve into the programs more thoroughly to accurately evaluate which program best met the needs of every student. The committee was extremely thoughtful about this. On our final day, representatives from the publishers were brought in to clarify, illustrate and answer final questions about this very concern. Specifically, Math Expressions was selected because it did provide the best resources to support all teachers in meeting the needs of all students in all classes. For addressing the needs of English Language Learners and struggling readers, Math Expressions offers: extensive visuals and hands-on resources, tips for supporting English Language Learners through instruction in teacher's manuals, Spanish translations of materials, including parent letters there is not excessive text yet there is enough text that the development of mathematical language skills is thorough instructional supports provided for teachers indicate how to tailor instruction for beginning, intermediate and advanced levels of ELL literacy connections,
differentiated writing prompts for each lesson Math Talks integrated into each lesson vocabulary scaffolding: introduction to vocabulary with suggestions for activities to use for instruction, teaching notes regarding vocabulary; graphic organizers; progression for vocabulary The committee felt that Math In Focus, while designed for use in Singapore with English instruction appeared to be more ELL friendly, it did not provide the balanced approach to learning both the numbers and the language of mathematics. Math Expressions provided a more balanced approach to all of the components of learning math in a systematic way. V. Is there enough repetition for practice and mastery of skills? We are used to seeing significant numbers of drill and practice problems in our math books. Will our students be ready for middle and high school? Math Expressions has a well-blended emphasis on fluency and application. We believe our students will be more prepared than ever to succeed in the Connected Math at the middle school and proceed on to the rigorous high school courses we offer in BVSD. In How the Brain Learns Math, David A. Sousa (Chapter 5, page 127) asserts to Limit the amount of material to practice. Practice should be limited to the smallest amount of material or skill that has the most relevancy for the students. This allows for sense and meaning to be consolidated as the learner uses the new learning. Remember that most preadolescents can deal with only about five items in working memory at one time. VI. Will our students need to be retaught in traditional algorithms before they can succeed in higher mathematics? Will our students receive a strong foundation in math for middle, high school and college? The CCSS are intended to provide students with depth of mathematical concepts rather than breadth. According to Phil Daro, college readiness means having a deeper understanding of core content. Through exploration and modeling of math, students are provided with the needed avenue to grasp the underlying reasons for how numbers are related. In his Colorado Council of Teachers of Mathematics 2011 Keynote speech, Phil Daro said, Correct answers are essential, but they re part of the process, they re not the product. The product is the math the kids will walk away with in their heads. MX is written to match the CCSS which are based in a mastery learning philosophy. Because the CCSS have identified a limited number of topics at each grade level, this will provide students the opportunity to achieve fluency with these concepts (Implementing a Common Core Curriculum, pg. 7). The over-arching goal of math in this district is to help students develop mathematical knowledge, conceptual understanding, and procedural skills, along with an awareness of the rich connections between math topics across grades and across content areas. Kim Bunning and David Webb, at the University of Colorado at Boulder have stated repeatedly in their
work with BVSD teachers that higher education is looking for students who have fluency in skills and the foundational understanding and the ability to apply the concepts that they know. How the Brain Learns Mathematics by David Sousa, Chapter 3, page 57. When students attempt to carry out simple arithmetic computations using memorized facts, they often jump to conclusions without considering the relevant conditions of the problem. They become so skilled at the mechanics of computation that they arrive at answers that do not make sense. Research Support: Teaching with the Brain in Mind, by Eric Jensen, Chapter 10, pages 92-93. Teachers who continue to emphasize one-sided lecture methods are violating an important principle of our brains. Essentially we are social beings and our brains grow in a social environment. Because we often forge meaning through socializing, the whole role of student-to-student discussion is vastly underused. When used properly, cooperative learning is highly brain compatible. Talking, sharing and discussing are critical; we are biologically wired for language and communicating with one another. Math Expressions has a balanced approach to fluency and application. We anticipate that students will emerge from our K-5 instruction with an even better number sense, fact fluency and conceptual understanding mix. VII. What is available to help parents support students at home? On-line support is available for parents and students. Parents will have access to videos that will support the introduction and summary of each lesson as well as specific examples. Buildings may provide information during conferences, Back-to-School Night, or may provide a Math Night as a means of providing further information. VIII. How will we ensure that the district s teachers have good foundation themselves for teaching in this manner? How can we collaborate to make sure we re implementing this well? In addition to the partnership with the program publisher, BVSD has developed an extensive professional development plan to ensure smooth and effective implementation and on-going support, including multiple opportunities for teacher collaboration and opportunities for teachers to explore content as a means for expanding their own understanding of concepts and best practices. BVSD has a PD plan for initial and on-going training provided by the district math department with support from Houghton Mifflin Harcourt publishers. This plan will also provide time for teacher collaboration. In addition, entire district focus days will be scheduled and the Elementary Math Specialist will be available to work with buildings and teachers on an as needed basis. IX. How will it be guaranteed that the program is being implemented with fidelity? Through professional development, teacher observation and collaboration time, district-level support and peerto-peer accountability, the implementation of Math Expressions will be done with fidelity and consistency.
X. Why didn t we pilot Math Expressions? Math Expressions is not a new program, both St. Vrain and Brighton have used it (Brighton since 2006) and have had excellent results with it. We did not pilot it because it was the committee who determined that they wanted to look at it - and that was in May 2012. XI. I have heard that students will no longer be accelerated in mathematics, even if they know all of the materials. Is this true? What will BVSD be doing to support these students? The changes in the standards will increase the level of challenge for every student. This transition will be one that requires individualization and special attention to an individual student s needs. For students who are talented, gifted, advanced or accelerated in their skills in mathematics, we are asking teachers to carefully assess the student s ability to not only demonstrate skills fluency, but also to ensure that the student has a full mastery (85% or higher) of the application of the skills. In the past, a student could be accelerated to the next grade level by demonstrating excellent skills fluency only. This is no longer sufficient the new standards call for deep understanding and ability to apply the skills in context. For this reason, we advise teachers, administrators and parents to use caution when considering acceleration of a student by skipping an entire grade level of material. We invite you to study the curriculum for the 5 th and 6 th grade mathematics courses to better understand the importance of the standards learned in these years. While we do anticipate that more students will accelerate in middle school, this does not limit the number of students who can or will accelerate. In fact, we believe that this will give more opportunities for students to accelerate as we will be able to identify students earlier and offer more opportunities for students to accelerate in middle school through the compacted courses M30 and M24. We will still have students who accelerate early in elementary and continue to coursework in Calculus 3 as seniors. As always, we will have individual students who follow a path that meets their specific needs and not a general path. Ask your school if they offer 6 th grade mathematics and how they will meet the needs of students who are ready for 6 th grade math in elementary school. Schools are asked to use a body of evidence collected throughout a student s mathematics career to help guide their recommendations for additional support or acceleration. The BVSD Universal K-5 Mathematics screeners, the Middle School Math Transition Assessment and the Algebra Readiness Assessment are three key tools that schools can use to collect evidence of student learning.