### Math interventions for situations where the student has not done the academic task that way before

ELM is a whole-class intervention designed for kindergarten students. ELM supports the mathematics learning of all kindergarten students, and research results indicate improved mathematics performance for students with and without mathematics difficulties.

Common Core Standards: Multiple

Setting: Whole Class

Focus Area: Acquisition, Fluency, Generalization

Academic or behavior problems may stem from lack of generalization. The student may know the skill but has not learned to generalize it to a new environment. This generalization technique utilizes consequences found naturally in or artificially added to the environment in order to promote generalization of behavior. There are four ways to exploit natural functional contingencies: identify natural consequences, recruit natural consequences, modify maladaptive consequences, and reinforce occurrences of generalization.

A graphic organizer is a tool used to facilitate student understanding of new mathematical concepts. Graphic organizers can help students organize their thinking and connect new information to prior knowledge. They provide visual representation for students to take notes on new mathematical concepts they are learning. Graphic organizers can be used in any setting, from whole group to individual, and students can use the practice every day.

Common Core Standards: Multiple

Setting: Whole Class, Small Group or Individual

Focus Area: Acquisition and Generalization

Academic or behavior problems may stem from lack of generalization. The student may know the skill but has not learned to generalize it to a new environment. This method incorporates teaching with artificial cues (cues that are not naturally used in generalizing environment) which include using physical object cues, social cues, self-regulated physical object cues, and self-regulated verbal cues.

The purpose of interleaving worked problems and problems to solve is to provide scaffolding through models or examples for students as they proceed through a set of math problems

Common Core Standards: Varied

Setting: Whole Class, Small Group, Individual

Focus Area: Acquisition, Fluency and Generalization

Full Intervention Brief: Interleaved Solutions and Problem Solving

Math PALS is a whole-class peer-tutoring program that can be used with students across grades K-6. With PALS, students work step-by-step on grade-level mathematics skills. The PALS model allows for students to practice mathematics skills with immediate feedback and to engage in discussion about mathematics.

Common Core Standards: Varied

Setting: Whole Class

Focus Area: Acquisition, Fluency and Generalization

Math Wise is a whole-class intervention for second-grade students. With Math Wise, students participate in lessons focused on addition and subtraction of single- and double-digit numbers.

Common Core Standards: Varied

Setting: Whole Class

Focus Area: Acquisition, Fluency and Generalization

Number Rockets is a small-group tutoring program for first-grade students experiencing mathematics difficulty. With Number Rockets, students participate in lessons focused on 17 topics (with 1-6 days of tutoring per topic) to help improve understanding of first-grade mathematics concepts and skills.

Common Core Standards: Multiple

Setting: Small Group and Individual

Focus Area: Multiple

*Pirate Math* is a program designed to improve the word-problem skill of elementary-aged students. Currently, there is a *Pirate Math *program for use in second-grade classrooms and a third-grade program for use as an individual tutoring intervention. During *Pirate Math*, students learn to

- Focus on and identify the conceptual framework of three types of word problems (i.e., Total, Difference, and Change word problems);
- Identify and ignore irrelevant information;
- Translate a word problem’s narrative to a mathematical equation, substituting “X” for the missing information;
- Solve for the missing variable (“X”) as expressed in the mathematical equation; and
- Self-evaluate the reasonableness of solved equations.

Common Core Standards: Varied

Setting: Whole Class and Individual

Focus Area: Acquisition, Fluency and Generalization

Overview:

Academic problems may stem from lack of generalization. The student may know the skill but has not learned to generalize it to a new environment. When that student naturally shows signs of generalization, reinforce the generalization.

ROOTS is a small-group tutoring program for kindergarten students experiencing mathematics difficulty. With ROOTS, students participate in 50 lessons focused on developing number sense to help improve understanding of kindergarten mathematics numbers and vocabulary. ROOTS is designed as a supplement to core instruction.

Common Core Standards: Multiple

Setting: Small Group

Focus Area: Acquisition, Fluency, Generalization

A schema is a way to organize or pattern information within a structured framework of known and unknown information. Within word-problem work, the learner identifies the type of problem (i.e., schema), which lends itself to solving the problem using a given organizational pattern. The main focus of Schema-Based Instruction or Schema-Broadening Instruction (SBI) is to teach word-problem solving using identification of a problem schema, representation using diagrams or equations to represent the schema, and solving the word problem. Scaffolding of student learning is provided throughout.

Common Core Standards: Operations and Algebraic Thinking (K-5), Numbers and Operations in Base Ten (K-5) and Numbers and Operations – Fractions (3-5)

Setting: Whole Class, Small Group or Individual

Focus Area: Acquisition, Fluency and Generalization

As indicated by Montague (2003), “The purpose of Solve it! Is to teach students to be good problem solvers.” Solve It! is a scripted curriculum designed to teach mathematical problem solving by engaging students in a series of steps that allow them to actively participate in metacognitive processing and demonstrate higher-order problem solving skills.

Common Core Standards: Multiple

Setting: Small Group or Individual

Focus Area: Acquisition and Generalization

Spring Math is a complete MTSS assessment and intervention system for mathematics for students in grades K-8 with remedial use in grades 9-12. Spring Math supports the mathematics learning of all students, and research results indicate improved mathematics performance for students with and without mathematics difficulties.

Academic or behavior problems may stem from lack of generalization. The student may know the skill but has not learned to generalize it to a new environment. Training and instruction can be adjusted to maximize potential for generalization. Trainers need to cautiously keep the balance between behavior acquisition (learning the behavior) and behavior robustness (how many environments can the trained behavior be used in?) Four ways to alter training in order to facilitate generalization: use sufficient stimulus exemplars, use sufficient response exemplars, make antecedents less discriminable, and make consequences less discriminable.

- Full Intervention Brief: Train Diversely

The purpose of a word problem mnemonic is to provide students with a framework for solving word problems. The mnemonic reminds students to work step-by-step through a word problem. Some word problem mnemonics can be used for problem solving beyond basic word problems.

Common Core Standards: Multiple

Setting: Whole Class, Small Group or Individual

Focus Area: Acquisition, Fluency and Generalization