Effective Instruction in Mathematics Across Tiers.

Effective Instruction in Mathematics Across Tiers

Using Data to Identify Student Need

State-Wide Data

National Math Advisory Panel Report (2008) American students have not been succeeding in the mathematical part of their education at anything like a level of an international leader. Particularly disturbing is the consistency of findings that American students achieve in mathematics at a mediocre level by comparison to peers worldwide. On our own National Report Cardthe National Assessment of Educational Progress (NAEP)--32% of our students are at or above the proficient level in Grade 8, but only 23% are proficient at Grade 12. Consistent with these findings is the vast and growing demand for remedial mathematics education among arriving students in four-year colleges and community colleges across the nation.

Effective Instruction in Math Provide explicit instruction to identify problem schemas Teach for transfer of skills to novel problem types Provide explicit instruction in problem-solving procedures Incorporate peer-mediated and independent practice opportunities Incorporate class-wide motivation strategies to promote engagement Instruction is provided from the concrete to representational/pictorial to abstract level

Effective Instruction in Math Utilization of tools and technology Content knowledge of teacher Combination of skill development and problem-solving Teaching for conceptual understanding, developing procedural literacy, and promoting strategic competence through meaningful problem-solving investigations Encourage divergent thinking Pose challenging questions Make interdisciplinary connections and examples Make math relevant!

Five Strands of Mathematical Proficiency Conceptual understanding-comprehension and connection of mathematical concepts Procedural fluency-skill to effectively/efficiently carry out procedures Strategic competence-formulating, representing, and solving Adaptive reasoning-logical thought, reflection, explanation, and justification Productive disposition-seeing math as useful and worthwhile (and ones own efficacy)

The Standards for Mathematical Practice 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning.

UDL Principles Application to Math Video

UDL Principles

Key Points About Motivating Math Students Student motivation is a combination of (1) expectation of success and (2) the value placed on success. Students may lack motivation because of previous lack of success Teachers can provide proactive feedback to students via (1) a course syllabus, (2) weekly assignment agendas, and (3) brief weekly student conferences. Academic Survival Skills Checklists can help students to develop self-management skills in organization, time management, and other areas. ~http://www.interventioncentral.org

Algebra as a Gateway Algebra is, in short, the gateway to success in the 21st century. What's more, when students make the transition from concrete arithmetic to the symbolic language of algebra, they develop abstract reasoning skills necessary to excel in math and science.

NMAP Recommendations Focused mathematics curriculum to meet the critical foundational needs for algebraic readiness Fluency with whole number computations Proficiency with fractions Aspects of geometry and measurement Core instruction IS NOT enough Explicit and systematic instruction Strategy instruction Conceptual understanding

Developing Effective Multi-Tiered Systems

Problem Solving Process

Utilizing Data ~National Center on Intensive Intervention (October 2013) Data from various sources interim (common assessment, annual statewide exams, commercially produced, end of course exams, interim tests developed by districts) and classroom (curriculum- based, projects, classwork, homework, observation). Data team to interpret data finding. Use data to measure intensity of the problem (gap analysis). Collaborative discussion among teachers regarding data use, student achievement and instruction. Students with similar needs may be grouped.

~University of Texas System/Texas Education Agency (2011)

Common Assessment

Brian Dean Senior Instructional Specialist, 6-12 Mathematics Office for Teaching and Learning Pasco County

Common Assessment

Common Assessment Design Developed collaboratively in PLCs Teams MUST be provided time to develop common assessments collaboratively Teams MUST be provided time to evaluate the assessments and determine instructional implications (e.g., decisions made reflective of the outcome data)

Math Common Assessment Example The following slides are: An example of a common assessment created through a PLC An example of a rubric developed by the PLC, which evaluates the common assessment An example of the data that is reflective of the common assessment

Algebra Case Study

CPALMS Algebra Example

MFAS Lesson Study Resource Kits Lesson study toolkits are supports for teachers engaging in the process of lesson study. MFAS has produced 20 lesson study resource kits for grades K - 3, Algebra, and Geometry. All these resource kits are aligned to the domains of the mathematics standards. These resource kits are available on the CPALMS.org website and interactively guide teachers through the stages of lesson study. Users will learn about each stage of lesson study as they are guided through its completion. The stages are: Form a lesson study team and orient to the process of lesson study. Negotiate and set student learning goals, Examine research on teaching and learning related to mathematical standards that you will teach, Plan a research lesson that will provide a window on student thinking, Teach and observe the lesson, Debrief the lesson by interpreting student data collected by your team; modify, reteach, and reflect on the lesson and the process, and Report and share the results of your lesson study experience. These resource kits are integrated with the Lesson Study Support System app within iCPALMS.

Tier 1

UDL and Math

National Library of Virtual Manipulatives Example for Algebra

StudentGradeSkill Deficit Javier45Computation of fractions Adam55Computation of fractions Janet52Computation of fractions Louie36Computation of fractions and number sense, as well as attention

Tier 2

Matching Intervention to Need

Key Points About Math Intervention The math teacher is the first responder The MTSS plan for math can include strategies for core instruction, academic intervention, and/or instructional adjustments (accommodations) There are resources which identify high-quality intervention programs

Data-Based Individualization Standards

Math Intervention Programs NCII-Study Quality

Math Intervention Programs NCII-Intensity

Math Intervention Courses Address foundational math skills Whole numbers Addition, Subtraction, Multiplication, Division and Decimals Address more in-depth skills Fractions and negative numbers Algebra, Geometry, Probability and Statistics Conceptual understanding, computational and procedural fluency and problem solving skills

Effective Instruction in Math Tier 2 A well-sequenced program of instruction that logically builds on existing skills and periodically returns to previously mastered skills to ensure maintenance Instructional design that eases the learning challenge Include opportunities for students to work with visual representations Increased opportunity for practice Cumulative review as part of increased practice Motivators to help students regulate their attention and behavior and to work hard Demonstration of correct and incorrect responses, and opportunities to practice performing newly learned skills with direct support (especially immediate corrective feedback) followed by more independent practice

Instructional/Intervention Design A comprehensive understanding of barriers to mastery of learning objectives allows for development of effective instruction and interventions For example: If student understanding of key mathematical vocabulary is a barrier then explicit pre-teaching of vocabulary should be included within the instructional design.

Components of Tier 2 Identify an instructional sequence Foundational Multiple opportunities to practice with the lessons Teach specific strategies Build procedural knowledge Increase student engagement Mastery Fluency Identify and teach prerequisite knowledge to build Error correction and scaffolds

Multiple Representations Concrete: Modeling/Guided Practice Counters Cubes Base-ten/Place value materials (units, rods, flats) Pictorial: Guided Practice/Independent Practice Five/ten frames Hundred charts Number lines Abstract: Guided Practice/Independent Practice Numbers Algorithms

National Library of Virtual Manipulatives nlvm.usu.edu nlvm.usu.edu

Illuminations by NCTM illuminations.nctm.org illuminations.nctm.org

Tier 2 Features Opportunities to make, show, write number concepts Enhance core curriculum through problem solving Regular, consistent intervention 4-5 days per week 20-30 minutes Progress monitoring Daily Independent practice 1-2 minutes Reflect material learned Weekly/Bi-weekly Aim checks Generalization

Fractions as Foundational Learning fractions is foundational to algebra The concept of a fraction is an abstraction Students typically learn fractions as a piece of pizza Students should simultaneously be introduced to fractions as a point on a number line

To Summarize Fractions are the main topic of the math curriculum in grades 57, and therefore naturally between the concrete arithmetic of whole numbers and the abstract considerations of algebra. If they are taught with mathematical integrity, they provide the needed introduction to abstract thinking, use of symbolic notation, and concept of generality.

Tier 3

Effective Instruction in Math Tier 3 Instruction should be more explicit and systematic. Interventions should include instruction on solving word problems that is based on common underlying structures. Use error-analysis data to identify instructional deficits and necessary adaptations Provide explicit instruction in foundational skills Increase math fluency Solving word problems using structured organizers Sequence for teaching fractional concepts Reciprocal peer tutoring Math centers

Where to Find High-Quality Tiers 2 and 3 Math Intervention Programs

What Works Clearinghouse http://ies.ed.gov/ncee/wwc/ http://ies.ed.gov/ncee/wwc/ This website reviews core instruction and intervention programs in mathematics, as well as other academic areas. The site reviews existing studies and draws conclusions about whether specific intervention programs show evidence of effectiveness. Best Evidence Encyclopedia http://www.bestevidence.org/ http://www.bestevidence.org/ This site provides reviews of evidence-based programs. The website is sponsored by the John Hopkins University School of Educations Center for Data-Driven Reform in Education (CDDRE). National Center on RtI http://www.rti4success.org/ http://www.rti4success.org/ Instructional Intervention Tools Chart Provides ratings to intervention programs across content areas. Users can sort their search by subject and grade level. Doing What Works http://dww.ed.gov/ http://dww.ed.gov/ This website is sponsored by the U.S. Dept. of Ed. and offers specific guidelines for how to teach effectively across content areas. The site has a section devoted to math, including pragmatic recommendations for putting into classroom practice the specific recommendations of the National Math Advisory Panel Report of 2008.

Aligning Tiers Utilize data to determine skill deficits Progress monitoring data Others? Intensify Instruction Identify intervention(s) that match student need Ensure alignment of intervention(s) to core instruction Provide generalizable strategies (e.g., C-R-A approach)

Missing Foundational Skills Fractions Number Sense

There Are No Quick Fixes

Contact Shelby Robertson, Ph.D. [email protected] 321-246-6550

Effective Instruction in Mathematics Across Tiers.

Documents

math video slide

efficacy slide

abstract level slide

student need slide

american students

statewide data slide

arriving students

effective instruction