Mathematics Barriers. Effective Approaches, Strategies and Supports

Transcription

1 Mathematics Barriers High Probability Barrier Number Sense The understanding of the relationship of quantity, value and numerical symbols or representations. These concepts help students understand the relationship among sets and allow students to make numerical comparisons. Observable Student Characteristics Observable ways that the barriers may hinder learning. Characteristics that may decrease access to and interaction with A student with weakness regarding number sense may: oneto-one correspondence not know relative values have difficulty using numbers to make judgments have difficulty knowing how to use numbers in a variety of ways when adding, subtracting, multiplying or dividing have difficulty developing useful strategies when counting, computational measurement or Effective Approaches, Strategies and Supports Provide a variety of objects to count, beginning with rote counting and eventually leading to rapid skip counting forward and backward. Have students be able to identify a quantity (1-10) without counting using dot cards (patterned and random) in early K-1 grades). Build competence with and understanding of numbers and their values. Build understanding of relationships between sets of objects (such as more, less, equal). Increase the ability to say and write the digits correctly. Increase understanding of math notation (+, -, =). Mode of Delivery Delivery mode describes the way instruction will be delivered to support and enable learning. Delivery mode will impact the way learners engage with the learning material and the way they experience the learning process within the core classroom. Teacher must provide direct, explicit, systematic Peer collaboration will encourage competency and understanding of numbers through practice. Technology will provide practice, as well as corrective feedback and progress monitoring. Across a Continuum Recommendations for support across tiers of Tier 1: Teacher meets the needs of all students through varied modes of delivery: -Whole Group (Direct, Explicit, Systematic Instruction) for building number sense. -Peer collaboration occurs to further ensure practice for understanding numbers and how to use them effectively across mathematical applications. -Technology is provided to further incorporate practice. Tier 2: Teacher meets with needs based groups which are created based on the analysis of data from formative assessment with the aim being for students to progress 1

2 estimating do not understand and use the vocabulary Increase the ability to use cardinal, ordinal, and nominal numbers. Use numbers lines to assist students with understanding magnitude of numbers for ordering and comparing, adding, subtracting, multiplication, division. Use Graphic organizers with manipulatives ( Part, Part, Whole or sectioned plates with rim to contain counters or manipulatives for younger children) Use Journals, Exit tickets, One-Sentence summaries to assist students in clarifying their understanding. Teach vocabulary using foldables, graphic organizers, identify meanings and related applications, actions, symbols, drawings, etc. toward completing the outcome or skill independently. greater intensity to build automaticity. Tier 3: Teachers have an opportunity for differentiated, small-group Meet with groups 1-3 times per week. This is an opportunity for teachers to provide enrichment for highperforming students. even greater intensity to build automaticity. 2

3 Task-Specific Barriers High Probability Barrier Fractions Observable Student Characteristics A student having difficulty with fractions may: that fractions can represent parts of a whole, parts of a group, or a ratio relationship. the meaning behind the numerator and denominator (What is the whole that is represented in this fraction?) part-whole partitioning the partitioning process misunderstand adding, subtracting, multiplying and Effective Approaches, Strategies and Supports Instruction should be focused on: conceptual knowledge of fractions (including percent) and proportional reasoning using models and number lines as much as possible for ordering and comparing including decimals, percent, improper fractions and mixed number as ordering and comparing on number line. procedural knowledge of fractions (including percent) and proportional reasoning (e.g, parts vs. whole, Mode of Delivery Teacher must provide direct, explicit, systematic Peer collaboration will increase conceptual understanding of fractions through multiple opportunities for practice. Technology will provide the opportunity to increase and mathematics Across a Continuum Tier 1: Teacher meets the needs of all students through varied modes of delivery: -Whole Group (Direct, Explicit, Systematic Instruction) to increase of fractions through multiple opportunities. -Peer collaboration occurs to further engage in activities, promoting of fractions through repetition. -Technology is provided to access multiple opportunities to increase and math Tier 2: Teacher meets with needs based groups which are created based on the 3

4 dividing of fractions the relationship between fractions, percents misunderstand factors and multiples and multiplication of whole numbers Can t visualize there are multiple representations of the same fraction (1/2, 2/4, 6/12, ) Can t compare and order fractions including improper, mixed, proper, and models of fractions. fraction representations to locations on a number line, fractions with magnitudes less than or greater than 1) Instruction should be focused on conceptual and procedural knowledge and should be reinforced and influenced by fractions (e.g., estimation, computation, solution of word problems). Instruction should include representational supports (e.g., ordering fractions on a number line). Use fraction tiles or circles or other manipulative to write equal fractions, add and subtract and subtract with renaming. Use virtual manipulatives for multiplying and dividing fractions. analysis of data from formative assessment with the aim being for students to progress toward completing the outcome or skill independently. greater intensity to access multiple opportunities to increase conceptual understanding of fractions through apps and math Tier 3: Teachers have an opportunity for differentiated, small-group Meet with groups 1-3 times per week. This is an opportunity for teachers to provide enrichment for high-performing students. an even greater intensity to access multiple opportunities to increase and math 4

5 Cross Content Barriers Which Can Be Addressed Through Core Instructional Strategies High Probability Barrier Observable Student Characteristics Effective Approaches, Strategies and Supports Attention Difficulties A student exhibiting attention difficulties may: Teach procedures connected to concepts Use visual, auditory, tactile, kinesthetic miss important info during instruction miss steps due to distractibility cues to point out important parts of a concept may be easily distracted by the environment Teach self-cuing strategies; highlight important info Provide self-tracking tally sheet to assist student with monitoring their own behaviors 5