Mastering Explicit Instruction - Part 4

By Dr. Deni Basaraba, RME Assessment Coordinator

We have come to an end on our series on explicit instruction (Please see our previous posts for more information!). Van de Walle (2013) characterizes explicit instruction as highly-structured, teacher-led instruction on a specific strategy. He explains how this approach can help uncover or make overt the thinking strategies that support mathematical problem solving for students with disabilities.

Here are our final thoughts on the elements necessary to carry out explicit instruction in the classroom.

Monitoring the performance of all students closely to verify students’ mastery of the content and help determine whether adjustments to instruction need to be made in response to student errors. Closely monitoring student performance can also help you determine which students are confident enough in their knowledge of the content to respond when signaled and which students are cueing off their peers by waiting for others to respond first.

Providing specific and immediate affirmative and corrective feedback as quickly as possible after the students’ response to help ensure high rates of success and reduce the likelihood of practicing errors. Feedback should be specific to the response students provided and briefly descriptive so that students can use the information provided in the feedback to further inform their learning (e.g., “Yes, we can use the written numeral 2 to show that we have two pencils”).

Delivering instruction at a “perky” pace to optimize instructional time, the amount of content that can be presented, the number of opportunities students have to practice the skill or strategy, and student engagement and on-task behavior. The pacing of content delivery should be sufficiently brisk to keep students engaged while simultaneously providing a reasonable amount of “think-time,” particularly when students are learning new material.

Providing distributed and cumulative practice opportunities to ensure that students have multiple opportunities to practice skills over time. Cumulative practice provides an opportunity to include practice opportunities that address both previously and newly learned content, skills, and strategies, facilitating the integration of newly learned knowledge and skills with previously learned knowledge and skills and supporting retention and fostering automaticity.

Thanks for joining us on our journey with explicit instruction! Please feel free to leave comments below with your thoughts or questions!

Baker, S. K., Gersten, R., & Lee, D. (2002). A synthesis of empirical research on teaching mathematics to low-achieving students. The Elementary School Journal, 103, 51-73.

Carnine, D. W. (1997). Instructional design in mathematics for students with learning disabilities. Journal of Learning Disabilities, 30, 130-141.

Doabler, C. T., Cary, M. S., Jungjohann, K., Clarke, B., Fien, H., Baker, S., Smolkowski, K., & Chard, D. (2012). Enhancing core mathematics instruction for students at risk for mathematics disabilities. Teaching Exceptional Children, 44, 48-57.

Van De Walle, J.A., Karp, K.S., & Bay-Williams, J.M. (2013). Elementary and middle school mathematics: Teaching developmentally, 8th edition. Boston: Pearson.

Witzel, B. S., Mercer, C. D., & Miller, M. D. (2003). Teaching algebra to students with learning difficulties: An investigation of an explicit instruction model. Learning Disabilities Research & Practice, 18, 121-131.

Mastering Explict Instruction - Part 3

By Dr. Deni Basaraba, RME Assessment Coordinator

We have been doing a series on how all students, particularly those who are struggling, benefit from the provision of explicit instruction (Baker, Gersten, & Lee, 2002; Carnine, 1997; Doabler et al., 2012; Witzel, Mercer, & Miller, 2003). Van de Walle (2013) characterizes explicit instruction as highly-structured, teacher-led instruction on a specific strategy. He explains how this approach can help uncover or make overt the thinking strategies that support mathematical problem solving for students with disabilities.

We started a list of the methods and elements of explicit instruction (see the previous two posts!). To continue this series of blogs, here are some additional elements of explicit instruction as well as examples and/or steps to carrying out these recommendations.

Using clear, concise, and consistent language that is not ambiguous, does not introduce irrelevant or unnecessary information into instruction, and is consistent across teacher models, whole group practice, and to elicit student responses so that students know what they are expected to do. Here are some suggestions to help with this element: Train interventionists to explain math content Include math concepts, vocabulary, formulas, procedures, reasoning and methods Use clear language understandable to students

Providing a range of examples and non-examples to help students determine when and when not to apply a skill, strategy, concept, or rule. Including a wide-range of positive examples during instruction provides students with multiple opportunities to practice the using the target strategy or skill while including non-examples can help reduce the possibility that students will use the skill inappropriately or over-generalize it to inappropriate mathematics problems. For example, here are some examples and non-examples of an algebraic expression: Example: Suppose we wanted to write an expression to find the total cost of movie tickets for different groups of people, given that tickets cost $7 each. We can define the variable "p" to represent the number of people in a group. Then the algebraic expression 7 x p or 7p represents the total cost of movie tickets for a group of p people. Non-example:The expression 550 + 20 is not an algebraic expression because it does not contain at least one variable.

Requiring frequent responses by relying minimally on individual student turns (e.g., asking students to raise their hand if they have the correct response) and relying more on the use of questioning to elicit various types of responses such as oral responses (e.g., having pre-identified partners or groups of students such as boys/girls, 1s/2s, apples/oranges respond), written responses, and/or action responses (e.g., thumbs up/thumbs down). Increasing the number of opportunities students have to respond during the lesson promotes a high level of student-teacher interaction, helps keep students engaged with the content, provides multiple opportunities for student practice with and elaboration on the newly learned content, and can help you monitor student understanding.

We have four more suggestions for mastering explicit instruction! Stay tuned!!

Baker, S. K., Gersten, R., & Lee, D. (2002). A synthesis of empirical research on teaching mathematics to low-achieving students. The Elementary School Journal, 103, 51-73.

Carnine, D. W. (1997). Instructional design in mathematics for students with learning disabilities. Journal of Learning Disabilities, 30, 130-141.

Doabler, C. T., Cary, M. S., Jungjohann, K., Clarke, B., Fien, H., Baker, S., Smolkowski, K., & Chard, D. (2012). Enhancing core mathematics instruction for students at risk for mathematics disabilities. Teaching Exceptional Children, 44, 48-57.

Van De Walle, J.A., Karp, K.S., & Bay-Williams, J.M. (2013). Elementary and middle school mathematics: Teaching developmentally, 8th edition. Boston: Pearson.

Witzel, B. S., Mercer, C. D., & Miller, M. D. (2003). Teaching algebra to students with learning difficulties: An investigation of an explicit instruction model. Learning Disabilities Research & Practice, 18, 121-131.

Mastering Explicit Instruction - Part 2

By Dr. Deni Basaraba, RME Assessment Coordinator

A couple of weeks ago, we discussed how all students, particularly those who are struggling, benefit from the provision of explicit instruction (Baker, Gersten, & Lee, 2002; Carnine, 1997; Doabler et al., 2012; Witzel, Mercer, & Miller, 2003). Van de Walle (2013) characterizes explicit instruction as highly-structured, teacher-led instruction on a specific strategy. He explains how this approach can help uncover or make overt the thinking strategies that support mathematical problem solving for students with disabilities. 

We started a list of the methods and elements of explicit instruction. To continue this series of blogs, here are some additional elements of explicit instruction as well as examples and/or steps to carrying out these recommendations.

Beginning each lesson with a clear statement of the objectives and goals for that lesson so that students know not only what they are going to learn but why it is important and how it relates to other skills and strategies they have already learned. For example: Today, we are going to continue our work with variables and expressions. You are going to learn how parentheses are used in expressions. You need this knowledge in order to solve algebraic equations.

Reviewing prerequisite knowledge and skills prior to starting instruction that includes a review of relevant information not only to ensure that students’ have the prior knowledge and skills needed to learn the skill being taught in the lesson but also to provide students an opportunity to link the new skills with other related skills and increase their sense of success. For example: First, let’s review. Tell your partner what a variable is. (A variable is a symbol that represents a number.) Yes, a variable is a symbol that represents a number. Look at these expressions (5 + x; t – 10). In the first expression, what is the variable? (X) Yes, x is a symbol that represents a number. Everyone, what is the variable in the second expression? (T) Let’s look again at the definition of an expression...

Modeling the desired skill or strategy clearly to demonstrate for students what they will be expected to do so and can see first-hand what a model of proficient performance looks like. When completing these models, think aloud for students so that each step of the strategy or skill you perform is clear and to clarify the decision-making processes needed to complete the procedure or solve the problem. For example: Look at this expression: 3 × ( 4 - 2). When an expression contains more than one operation, parentheses can be used to show which computation should be done first. So, when we have an expression, we first look for parentheses and do the operation inside the parentheses. In this problem, 4 - 2 is inside the parentheses, so I will do that operation first...

Providing guided and supported practice by regulating the difficulty of practice opportunities from easier to more challenging and providing higher levels of guidance and support initially that is gradually decreased as students demonstrate success. For example: Let’s do some problems together. Please stay with me so we can do these items correctly. Write this expression on your paper, but don’t solve it. Do we do the operations inside or outside of the parentheses first...  Write this expression on your paper. Do we do the operations inside or outside of the parentheses first? Inside. Find the value of the expression. (After several examples where the teacher slowly gives less help) Copy this expression and find the value of the expression. Don’t forget . . . parentheses first...

Baker, S. K., Gersten, R., & Lee, D. (2002). A synthesis of empirical research on teaching mathematics to low-achieving students. The Elementary School Journal, 103, 51-73.

Carnine, D. W. (1997). Instructional design in mathematics for students with learning disabilities. Journal of Learning Disabilities, 30, 130-141.

Doabler, C. T., Cary, M. S., Jungjohann, K., Clarke, B., Fien, H., Baker, S., Smolkowski, K., & Chard, D. (2012). Enhancing core mathematics instruction for students at risk for mathematics disabilities. Teaching Exceptional Children, 44, 48-57.

Van De Walle, J.A., Karp, K.S., & Bay-Williams, J.M. (2013). Elementary and middle school mathematics: Teaching developmentally, 8th edition. Boston: Pearson.

Witzel, B. S., Mercer, C. D., & Miller, M. D. (2003). Teaching algebra to students with learning difficulties: An investigation of an explicit instruction model. Learning Disabilities Research & Practice, 18, 121-131.

Mastering Explicit Instruction - Part 1

By Deni Basaraba, RME Assessment Coordinator

Research (Baker, Gersten, & Lee, 2002; Carnine, 1997; Doabler et al., 2012; Witzel, Mercer, & Miller, 2003) indicates that all students, but particularly struggling learners, benefit from the provision of explicit instruction, which can be defined as a direct an unambiguous approach to instruction that incorporates instructional design and instructional delivery procedures (Archer & Hughes, 2011).

Moreover, students benefit from having strategies for learning content made conspicuous for them but only when these strategies are designed to support the transfer of knowledge from the specific content being taught (i.e., the mathematics problems that are the focus of instruction during a particular class period) to a broader, more generalizable context (e.g., similar mathematics problems with similar or more complex types of numbers, similar mathematics problems presented during whole group instruction to be solved collaboratively, in pairs, or independently as part of homework) (Kame’enui, Carnine, Dixon, & Burns, 2011).

What is explicit instruction?

As noted previously, the idea of explicit instruction includes both instructional design and instructional delivery features, and requires that we carefully consider not only the content we plan to teach and the order in which that content is sequenced but also the methods we used to deliver that instruction to our students. In this series of blogs, we will provide you with elements of explicit instruction as well as examples and/or steps to carrying out these recommendations.

Focusing instruction on critical content (e.g., skills, strategies, concepts, vocabulary) that is essential for promoting student understanding of the target content as well as future, related content. The amount of time designated each day to explicit vocabulary instruction will depend upon the vocabulary load of the text to be read as well as the students’ general prior knowledge of the new vocabulary.  Computer-assisted instruction can be another effective way to provide practice on newly-introduced vocabulary words.  Other methods include using graphic organizers and semantic maps to teach the relationships among words and concepts.

Organizing instruction around “big ideas” that can help students see how particular skills and concepts fit together. This will provide students with a clearer understanding of how content, skills, and strategies are related and can help students organize that information in their minds, making it easier for them to retrieve that information and integrate it with new material. Example: Fractions are numbers that can be represented in different ways. Modeling part/whole relationship Writing fraction numbers Comparing fractions Measuring fractions on a number line

Sequencing skills in a logical fashion so that (a) students learn all prerequisite skills before being asked to perform the target skill, (b) high-frequency skills are taught before those needed less frequently, (c) skills and strategies that are similar and may be confusing to students are not taught in close proximity within the scope and sequence, and (d) easier skills are taught before more difficult skills.

Breaking down complex skills and strategies into smaller units in an effort to minimize cognitive overload and the demands placed on students’ working memory. Teach skills in small, discrete steps that can be added to one another to form the target skill. Present new information in small steps will give students enough to have success on the topic.  Once students have mastered that step, reinforce the topic and add to it.

Archer, A. L, & Hughes, C. A. (2011). Explicit instruction: Effective and efficient teaching. New York NY: Guilford.

Baker, S. K., Gersten, R., & Lee, D. (2002). A synthesis of empirical research on teaching mathematics to low-achieving students. The Elementary School Journal, 103, 51-73.

Carnine, D. W. (1997). Instructional design in mathematics for students with learning disabilities. Journal of Learning Disabilities, 30, 130-141.

Doabler, C. T., Cary, M. S., Jungjohann, K., Clarke, B., Fien, H., Baker, S., Smolkowski, K., & Chard, D. (2012). Enhancing core mathematics instruction for students at risk for mathematics disabilities. Teaching Exceptional Children, 44, 48-57.

Kame’enui, E. J., Carnine, D. W., Dixon, R. C., & Burns, D. (2011). Introduction. In M. D. Coyne, E. J. Kame’enui, & D. W. Carnine (Eds.) Effective teaching strategies that accommodate diverse learners (4th ed.) (pp. 7-23).

Witzel, B. S., Mercer, C. D., & Miller, M. D. (2003). Teaching algebra to students with learning difficulties: An investigation of an explicit instruction model. Learning Disabilities Research & Practice, 18, 121-131.