Direct Instruction Mathematics

Description of the Strategy

Direction instruction (DI) mathematics is an approach to teaching mathematics that is characterized by its distinctive instructional delivery and efficient instructional design. The theory of direct instruction is that all students can learn if they are provided with welldesigned, systematic, and research-validated curricula and if teachers take responsibility for student learning.

Unique features of DI instructional delivery include explicit teacher-directed instruction, high levels of teacher-student interactions, and teaching students to mastery. Commercially published lessons using this approach include detailed scripts of what the teacher says and does and what students are to say and do. Example problems are carefully selected and sequenced. Initial instruction is highly teacher directed and explicit, with the teacher modeling skills and explaining steps of complex strategies. After the teacher provides a model of what students are supposed to do, students then practice under the teacher's immediate supervision, with guidance to minimize errors. The teacher prompts the students in the steps of the strategy, and students respond verbally or in writing. This prompting provides students with enough positive practice that mastery can be achieved. Guidance and support is decreased slowly until students can discriminate when to apply the new skill or strategy and demonstrate success without teacher prompting. Only then are students allowed to practice on their own to develop fluency. This process often takes multiple lessons.

Instructional design is another distinguishing feature of DI mathematics. Based on Siegfried Engelmann's theory of instruction, six instructional design principles guide DI mathematics: (a) teach the big ideas, (b) model explicit strategies, (c) provide scaffolded supports to guide students during initial stages of learning, (d) connect new learning to students' prior knowledge, (e) strategically integrate new learning so students can select how and when to use the new strategy or can combine the new strategy with other strategies, and (f) provide systematic practice and review so students develop fluency and generalize knowledge to new problems and contexts.

Teaching big ideas entails carefully analyzing math content and identifying and prioritizing important math knowledge. These big ideas are organized into strands (or math topics) similar to the topics found in the widely recognized National Council of Teachers of Mathematics (NCTM) Standards. DI strands include counting, symbol identification, place value, operations (addition, subtraction, multiplication, and division), fractions, solving problems, measurement, [Page 1264]geometry, decimals, percentages, ratios and proportions, coordinate systems, and probability.

These strands are further broken down into instructional sequences or logical hierarchies of subskills and sequenced by grade level. For example, the strand of symbol identification and place value begins at the kindergarten (K) level with the skill of reading and writing numbers to 10 and making sets equivalent to numbers 1 through 10. First-grade skills include reading and writing numbers to 100, column alignment, and expanded notation. Second-grade skills extend number concepts to 1000, third grade to 10,000, fourth grade to millions numbers, and fifth grade to numbers beyond millions. The operations strand starts in first grade, with conceptual addition and subtraction, followed by addition and subtraction of singledigit numbers, fact memorization, and column addition and subtraction with renaming, and it continues through fourth grade, with addition and subtraction with multiple and larger numbers. Some strands, such as decimals, percentages, and ratios, start in the intermediate grades (fourth and fifth).

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