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Curriculum Evaluation ReportSeptember 24, 2019Kristie ChandlerSTEM 661Mathematics Specialists as Teacher Leaders Curriculum0317500Big Ideas Math: Modeling Real LifeLarson, R., Boswell, L. (2019)Ideas Learning L.L.C.Grade 5Below is a lesson from an upcoming chapter in the textbook. The layout of the student’s edition guides the students through the lesson. The learning target and success criteria are easy to spot and to understand. The language of the success criteria is found throughout the lesson. As the student’s understanding increases, so do the level of the problems they are presented. Each lesson has the following features in the student’s edition. Chapter Lessons in Student’s EditionLayout FeatureDescriptionLearning Target and Success CriteriaDescribes what students will learn and what they should be able to do by the end of the lesson. These allow for tracking of student progress and help with motivation and engagement. Explore and GrowProvides students either a concrete or semi-concrete approach to build conceptual understandingThink and GrowAllowing for teacher-guidance to break down the conceptShow and GrowProvides a brief formative assessmentApply and GrowPractice with the conceptThink and GrowProblem-solving version of Think and Grow brings in real-life examples of how to apply the conceptHomework/Practice Have a QR code that links to lessons pages to assist with understand concepts. The organization of the teacher’s edition guides the instructor from preparing for the lesson, instructing the lesson, and concluding it. Multiple options are listed throughout the teacher’s plans to meet the needs of learners. Each lesson has the following features in the teacher’s edition.Chapter Lessons in Teacher’s EditionLayout FeatureDescriptionPreparing to Teach An overview portion about the math concepts for the chapter to assist with the teacher’s understanding; explanation of the strands in the lessons, background information for the concepts, and detailed examples.Dig In (Motivate Time)This acts as the hook for the lesson, aiming to grab the students’ attention through investigating concepts through manipulatives, games, or other interactive strategies.Learning Target and Success CriteriaWith notes to aid in scaffolding instructionExplore and Growprovides students either a concrete or semi-concrete approach to build conceptual understandingThink and Growallowing for teacher-guidance to break down the conceptShow and Growprovides a brief formative assessmentApply and Growpractice with the conceptThink and Growproblem-solving version of Think and Grow brings in real-life examples of how to apply the conceptClosure Suggestions for wrapping up the lesson and a formative check on learning Connect and Extend Learning Provides options for connecting concepts to other content areas and extending learning for those who have shown mastery. Homework/Practice Contains multiple practice problems for the concepts for all levels of understanding. For a “concept check”, certain problems are identified to have the students complete. The curriculum identifies the major topics, supporting topics, and additional topics in the table of contents in each grade level edition. Most of the content standards are part of the instruction for each grade level; however, there are some that are not covered at all in a certain grade level. Due to this, teachers will have to locate supplemental curriculum to use for those gaps. Some of those supplemental resources can be pulled from a different grade level, while other resources will have to be found outside of the Big Ideas curriculum. Content Standards from NCTMStandard Major TopicSupporting TopicAdditional TopicNumbers and OperationsK, 1st, 2nd, 3rd, 4th, 5th, 6th, 7th 8th 3rd3rd, 5th, 6th 8thAlgebraK, 1st, 2nd, 3rd, 4th, 6th, 7th 8th5th , 8th5th, 6th, 8thGeometry 8th K, 2nd, 3rd, 4th 1st, 2nd, 3rd, 4th, 7th, 8th Measurement1st, 2nd, 3rd, 5th 6th 1st, 4th 5th 6th K, 4th 6th, 7th 8thData Analysis & Probability 1st, 2nd, 3rd, 5th1st, 2nd, 7th , 8th5th 6th, 7th , 8thOverall, the curriculum provides lots of support for the teacher to guide students to demonstrate the process standards. Features are embedded in each lesson and throughout the chapter. The curriculum does not provide as many opportunities for problem solving, until students have mastered or almost mastered the concept. Supplemental resources would be needed for that process standard (problem solving) with some topics in the curriculum. The table below summaries the features in the curriculum that include the process standards. Process Standards from NCTMStandard Curriculum Feature(s)Problem Solving:Build new mathematical knowledge through problem solvingSolve problems that arise in mathematics and in other contextsApply and adapt a variety of appropriate strategies to solve problemsMonitor and reflect on the process of mathematical problem solvingAttend to Precision – poses scenarios of “what if…” to encourage discussion of the accuracy of strategies Logical-Mathematical – create and solve problems to extend student learning Reasoning and Proof:Recognize reasoning and proof as fundamental aspects of mathematicsMake and investigate mathematical conjecturesDevelop and evaluate mathematical arguments and proofsSelect and use various types of reasoning and methods of proof?Reason Abstractly and Quantitatively – found in some lessons in the Teaching Notes. Look for and Express Regularity in Repeated Reasoning – found in some lessons, making connections in reasoning of different problems/scenariosCritique the Reasoning of Others - ideas for questions to encourage student critiquesCommunication:Organize and consolidate their mathematical thinking through communication?Communicate their mathematical thinking coherently and clearly to peers, teachers, and othersAnalyze and evaluate the mathematical thinking and strategies of others;Use the language of mathematics to express mathematical ideas precisely.??Turn and Talk – each lesson has suggestions for question prompts for students to discuss concepts togetherThink-Pair-Share – concepts and questions to encourage student discourse ? – questions to guide discussions, ordered in a way to build conceptual understandingConstruct Viable Arguments – ideas for questions to ask students to guide mathematical arguments Critique the Reasoning of Others – ideas for questions to encourage student critiques Connections:Recognize and use connections among mathematical ideasUnderstand how mathematical ideas interconnect and build on one another to produce a coherent wholeRecognize and apply mathematics in contexts outside of mathematicsConnection – in each lesson, for similar concepts and strategies Cross-Curricular Connections – provides scenarios where students can apply the math concepts they are learning to topics in social studies, science Look for and Make Use of Structure – questions about patterns in conceptsRepresentationsCreate and use representations to organize, record, and communicate mathematical ideasSelect, apply, and translate among mathematical representations to solve problemsUse representations to model and interpret physical, social, and mathematical phenomena?Math Manipulatives - fraction blocks, unifix cubes, cuisenare rods, base-ten blocks, etc. Math Tools – online interactive manipulatives, graphic organizers, charts, tables, etc. Use Appropriate Tools Strategically – found in some of the lessons, questions and explanations for when and how to use tools and modelsThe principles for school mathematics are present throughout the curriculum. Overall, Big Ideas adequately addresses each of the principles. There are numerous levels and types of instructional resources to choose from. For the principle of teaching, a more user-friendly guide would be beneficial to help the teacher effectively select resources to use in order to best meet students’ needs. Suggestions are provided throughout the lessons and chapters, however, they are spread out and not found in a central location. Principles for School Mathematics from NCTMPrinciple Curriculum Feature(s)Equity:Excellence in mathematics education requires equity—high expectations and strong support for all students.Scaffolding Instruction is provided in each lesson. Suggestions are given for emerging and proficient learners. Notes also include connections to prior knowledge, multiple approaches of representations, support language for ELL students, ELL Support – questions, vocabulary, common errors, modifications, etc. for ELL studentsAssignment Guide – provides multiple options for formative and summative assessments, that can be modified to meet student needsConcept Check – helps to identify problems that can be used to check comprehension of concepts Differentiating the Lesson – in each chapter, multiple lessons have variations of the lessons to meet the needs of emerging and advanced studentsResponse to Intervention – guide to which resources are best used for the different tiers of response to intervention and when and how to use themMath Musicals – plays, stories, and songs to deepening understanding of concepts and make real-world connections Vocabulary – important math terms for the chapter, lessons, and different types of learners Teacher and Student Editions - in English and Spanish Curriculum:A curriculum is more than a collection of activities: it must be coherent, focused on important mathematics, and well articulated across the gradesProgressions Through the Grades – similar/related standards and concepts throughout the grade levels and how they are connected and build upon each otherPacing Guide – suggestions for how to pace out the chapter’s lessons based on difficultly level and amount of timeChapter Overview – provides the teacher with explanations and examples of important topics for the chapterAbout the Math - provides the teacher with explanations and examples of important concepts for the lessonOnline resources can be narrowed by the type needed (planning, teaching, ancillaries, RTI, and answers)Access to all grades - teacher and student resourcesResources for Kindergarten through 8th grade, Geometry, Algebra 1 and Algebra 2Teaching:Effective mathematics teaching requires understanding what students know and need to learn and then challenging and supporting them to learn it mon Error – found in most lessons and provide the teacher with a heads-up of what kind of errors are common for the concepts.Lesson Resources – are labeled with the DOK (Depth of Knowledge) level Teaching Tip – each lesson provides suggestions of modifications or adjustments that can be made to assist with instruction and student learningLearning:Students must learn mathematics with understanding, actively building new knowledge from experience and prior knowledge.Prior Skills – provides information from other chapters and gradesCross – Curricular Connections - provides scenarios where students can apply the math concepts they are learning to topics in social studies, science The lessons do build upon each other, so for the majority of the chapters, the lessons must be taught in order. Preview – included in each lesson, suggestions for accessing and/or building background knowledgeAssessment:Assessment should support the learning of important mathematics and furnish useful information to both teachers and students.All assessments are editable - questions can be added, taken away or reworded to fit the needs of the students and the instruction. Various types - Course Benchmarks, Pre- and Post-Course Tests, Prerequisite Skills TestOnline formative checks with each lesson (Explore and Grow, Show and Grow, Apply and Grow sections) allow the teacher to monitor students’ progress as they complete problems on the computer and the students to check their answer and receive helpReports – for performance, standards, and skills trainerTechnology:Technology is essential in teaching and learning mathematics; it influences the mathematics that is taught and enhances students' learning.The technology package that comes with the series, Dynamic Classroom, provides additional options for the teacher, students, and parents. For the teacher – assignments, formative assessments, Skills Trainer, reports, Teacher Support VideosFor the students – Math Tools, Skills Trainer, Game Library, Math Musicals (all of which interest students) For the parents – QR Codes, Game Library, flash cards, digital examples, interactive explorationsSummary of VA SOL AddressedThe following is based upon the developing fifth grade mathematics-pacing guide from my school district. This information is a combination of work from the math committee I served on, a summer workday I participated in, and our elementary math specialist. The majority of the Virginia Standards of Learning for Fifth Grade Mathematics are found in the curriculum. There are some that are either not sufficiently covered or not covered at all in the grade level. Supplemental resources will be needs for some of the SOLs. The table below summaries the SOLs addressed in the curriculum.5th Grade Pacing School Week Content SOL EKS to embed Notes1-3Chapter 1: Place Value Concepts5.1 5.2a 5.2b?● 5.2a provide additional opportunities for students to see fractions and decimals in concrete forms ● 5.2a provide opportunities for students to represent fractions that have denominators of thirds and eighths, as well as halves, fourths, fifths, twentieths, twenty-fifth and fiftieths (factors of 100) in their equivalent decimal form ● The rest of 5.2 will be covered in between chapter 7 and 8. ● Chapter 1 covers: finding 10 times a number (UTS) finding 1/10 of a number (UTS) expanded form of whole numbers comparing whole numbers using exponents to show powers of 10 comparing decimals ordering decimals4-5Chapter 2: Numerical Expressions5.7Embed after lesson 2.4 ● 5.7 Given a whole number numerical expression involving more than one operation, describe which operation is completed first, which is second, etc.Lesson 2.4 introduces different types of grouping symbols6-8Chapter 3: Add and Subtract Decimals5.5b9Prime and Composite, Even and Odd5.3abBIM 4th grade lesson 6.4 covers prime and composite10-11Chapter 4: Multiply Whole Numbers5.4Chapters 4 & 6: Include opportunities for students to create and solve single step and multistep practical problems involving addition, subtraction, multiplication and division of whole numbers (5.4) needs to be embedded.12-14Chapter 5: Multiply Decimals5.5abThe parameters in this chapter go beyond 2 digit x 2 digit and the products go beyond the thousandths place.15-17Chapter 6: Divide Whole Numbers5.45.4 Use the context of a practical problem to interpret the quotient and remainder18-20Chapter 7: Divide Decimals5.5bChapters 5: Include opportunities for students to create and solve single step and multistep practical problems involving addition, subtraction, and multiplication of decimals (5.5b) Chapters 7: Include opportunities for students to create and solve single step practical problems involving division of decimals (5.5b)21Fraction and decimal equivalencies5.222-24Chapter 8: Add and Subtract Fractions5.6a25Chapter 9: Multiply Fractions5.6bEmbed after lesson 9.3 ● 5.6 b Apply the inverse property of multiplication in models. (For example, use a visual fraction model to represent 4/4 or 1 as the product of 4 x ?)Lessons 9.4-9.8 involve multiplying fractions by fractions.26-27Algebra5.1928-29Chapter 11: Convert and Display Units of Measure5.9 5.11 5.16 5.1711.7 covers the line plot portion of SOL 5.16a and b. The stem-and-leaf plot portion of this standard, as well as 5.16c (compare data represented in a line plot with the same data represented in a stem-and-leaf plot) will need to be embedded after 11.7It would be beneficial to teach in the following order 11.1, 11.2, 11.6 Stem-and-Leaf plots 11.7, 11.830-31Mean, Median, Mode, and Range5.1732Chapter 12: Patterns in the Coordinate Plane5.18Lesson 12.6 covers patterns although additional lessons on patterns will need to be embedded12.1-12.5 and 12.7 involve Coordinate planes33Probability5.1534Perimeter and Area5.8ab35Chapter 13: Understand Volume5.8After lesson 13.4, embed a lesson on differentiating among perimeter, area, and volume and identify whether the application of the concept of perimeter, area, or volume is appropriate for a given situation.13.5 involves finding the volume of composite figures36-38Chapter 14: Classify two-dimensional shapes5.10 5.12 5.13 5.14Embed the following essential knowledge and skill after 14.1 ● 5.13b Use models to prove that the sum of the interior angles of a triangle is 180 degrees, and use that relationship to determine an unknown angle measure in a triangle ● 5.10 All essential knowledge and skills ● 5.14 All essential knowledge and skills5.12 is covered in the vocab section at the beginning of the chapterNote: Chapter 10 covers dividing fractions. For pacing purposes, save this chapter for enrichment at the end of the school year.Evaluation of Mathematics Curriculum RubricNote: Adapted from Common Core State Standards (CCSS) Mathematics Curriculum Materials Analysis ProjectKey:Not Found (N) - The curriculum materials do not support this element.Low (L) - The curriculum materials contain limited support for this element, but the support is not embedded or consistently present within or across grades.Medium (M) - The curriculum materials contain support for this element, but it is not always embedded or consistently present within or across grades.High (H) - The curriculum materials contain embedded support for this element so that it is consistently present within and across grades.Questions about Overarching ConsiderationsSee Rubric To what extent do the materials:N-L-M-HProvide alignment with the VDOE SOLs?MProvide teachers with strategies for meeting the needs of a range of learners?HProvide instructional support to help teachers sequence or scaffold lessons so that students move from what they know to what they do not know?HProvide opportunities for teachers to use a variety of grouping strategies?MEmbed tasks with multiple entry-points that can be solved using a variety of solution strategies or representations?MSupport the development of students’ mathematical understanding?HSupport the development of students’ proficiency with procedural skills? MAssist students in building connections between mathematical understanding and procedural skills?MDo student activities build on each other within and across grades in a logical way that supports mathematical understanding/procedural skills?HProvide opportunities to use reading, writing, and speaking in mathematics lessons.HEncourage teachers to draw on multiple resources such as objects, drawings, and graphs to facilitate learning?HProvide opportunities for teacher and students to connect mathematics to other subject areas?MProvide both individual and collective opportunities for students to learn using mathematical tasks with a range of challenge?MProvide opportunities for advanced students to investigate mathematics content at greater depth?HAssessmentTo what extent do accompanying assessments of student learning (such as homework, observation checklists, portfolio recommendations, extended tasks, tests, and quizzes) provide evidence regarding students’ proficiency?MProvide strategies for gathering information about students’ prior knowledge and background?MProvide strategies for teachers to identify common student errors and misconceptions?MAssess students at a variety of knowledge levels (e.g., memorization, understanding, reasoning, problem solving)?HEncourage students to monitor their own progress?HProvide opportunities for ongoing review and practice with feedback related to learning concepts, and skills.MProvide support for a varied system of on-going formative and summative assessment (formal or informal observations, interviews, surveys, performance assessments, target problems)?HTechnologyIntegrate technology such as interactive tools, virtual manipulatives/objects, and dynamic mathematics software in ways that engage students.HInclude or reference technology that provides opportunities for teachers and/or students to communicate with each other (e.g. websites, discussion groups, webinars)?LInclude opportunities to assess student mathematical understandings and knowledge of procedural skills using technology?HInclude or reference technology that provides teachers additional tasks for students?MInclude teacher guidance for the mindful use of embedded technology to support and enhance student learning?MOverall EvaluationM/HSummary Discussion QuestionsEquity: To what extent do the materials contain embedded support for elements of equity consistently within and across grades?Assessment: To what extent do the materials contain embedded support for elements of assessment consistently within and across grades?Technology: To what extent do the materials contain embedded support for elements of technology consistently within and across grades?Overall: To what extent do the materials incorporate the Overarching Consideration elements to advance students’ learning of mathematical content and engagement in the mathematical practices?Content Coverage Rubric (Cont):Not Found (N) - The mathematics content was not found.Low (L) - Major gaps in the mathematics content were found. Marginal (M) - Gaps in the content, as described in the Standards, were found and these gaps may not be easily filled.Acceptable (A) - Few gaps in the content, as described in the Standards, were found and these gaps may be easily filled.High (H) - The content was fully formed as described in the Standards.Balance of Mathematical Understanding and Procedural Skills Rubric (Bal):Not Found (N) - The content was not found. Low (L) - The content was not developed or developed superficially.Marginal (M) - The content was found and focused primarily on procedural skills and minimally on mathematical understanding, or ignored procedural skills.Acceptable (A) -The content was developed with a balance of mathematical understanding and procedural skills consistent with the Standards, but the connections between the two were not developed.High (H) - The content was developed with a balance of mathematical understanding and procedural skills consistent with the Standards, and the connections between the two were developed.ResourcesCouncil of Chief State School Officers, Brookhill Foundation, and Texas Instruments. (2011). Common Core State Standards (CCSS) Mathematics Curriculum Materials Analysis Project Retrieved from , R., Boswell, L. (2019). Big Ideas Math: Modeling Real Life. Erie, Pennsylvania: Big Ideas Learning L.L.C. Retrieved from Department of Education. (2016) Mathematics Standards of Learning for Virginia Public Schools. Retrieved from Public Schools (2019). Big Ideas Alignment Document. Waynesboro, VA. Retrieved from ................
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