This white paper summarizes the proceedings of a summit that was focused on integrating research knowledge on promising approaches into intensive intervention and implementation to improve academic outcomes for students with disabilities who have severe and persistent learning need. In addition, it includes responses from three participants representing perspectives from policy (David Chard, Wheelock College), research (Nathan Clemens, University of Texas at Austin), and practice (Steve Goodman, Michigan Integrated Behavior and Learning Support Initiative).
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This report presents findings from an exploratory study of how five high-performing districts, which we refer to as NCII’s knowledge development sites, defined and implemented intensive intervention. The findings offer lessons that other schools and districts can use when planning for, implementing and working to sustain their own initiatives to provide intensive intervention for students with the most severe and persistent learning and/or behavioral needs.
This video describes how to use the partial sums strategy with addition. The problem in this video requires regrouping; however, the partial sums strategy eliminates the regrouping procedure. The partial sums strategy is typically performed left to right and focuses on adding only part of each multi-digit number at a time (e.g., only adding digits in the hundreds column to determine the partial sum of hundreds, followed by only adding digits in the tens column to determine the partial sum of tens, and so on). It may be especially important for students to know and understand the partial sums strategies if they have not yet developed an understanding for regrouping. This strategy is also efficient when all or most of the numbers have the same number of digits.
This video uses manipulatives to review the five counting principles including stable order, correspondence, cardinality, abstraction, and order irrelevance.
This video illustrates how to use the traditional algorithm to solve subtraction with regrouping. The traditional algorithm focuses on digit placement and requires that students move right to left to correctly perform the operation. Before students are introduced to the standard addition algorithm, it is important that they have a conceptual understanding of regrouping. This will allow students to correctly use the algorithm when they exchange 10 ones in the ones place value column with 1 ten in the tens place value column. It is important for students to know and understand how to use the traditional algorithm because it is an efficient strategy to use if regrouping is required, when numbers have varying numbers of digits, and when the numbers included are too large to reasonably use other strategies (e.g., partial differences can become confusing for students who do not understand negative integers).
This video describes how to use the partial differences strategy to solve multi-digit subtraction.
This video reviews to how use the traditional algorithm to solve multiplication with regrouping.
In this video, Derrick Bushon, Director of Student Services for Swartz Creek Community Schools, discusses how his district took a systems approach to integrating DBI into schools.
This video illustrates the use of scaffolding with manipulatives to teach students to group objects by tens with counting by ones.
This video illustrates the use of an efficient counting on strategy that students may practice to solve simple addition problems without the use of manipulatives. When students use a counting on strategy to solve an addition problem, they must be able to hold one number in working memory; however, an important working memory strategy to teach students and allow students to practice includes using fingers to track counting. Counting on is an efficient strategy that students may use to quickly determine the solution to an addition problem. With enough practice opportunities students will soon be able to perform simple arithmetic without the use of working memory strategies such as finger counting.