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INTERVENTION

It is recommended that Math Coaches and teachers participate in training and have access to continued support in the use of the Assessing Math Concepts (AMC) assessments and Developing Number Concepts (DNC) lessons to provide individual and small group, differentiated instruction as targeted classroom interventions to students struggling in math. Classroom teachers and Special Education teachers using the Assessing Math Concepts (AMC) assessments and the Developing Number Concepts series for their instruction will be able to provide high quality instruction and/or intervention matched to the student needs. Teachers using these assessments and instruction will be able to intervene early and use a multi-tier intervention/teaching model.
Using the Assessing Math Concepts (AMC) assessments for Intervention
This series of assessments allows the teacher to monitor student progress and inform their instruction. They can be used to identify the needs of individual students who are having difficulty with the mathematics the rest of the class is working on. When assessing an individual student, the goal is to find the “edge of the child's understanding” in order to provide appropriate instruction that can build on what the child already knows. Often a child needs prerequisite skills to prepare him or her for instruction with the concept the class is working with. The following is a brief suggestion of a place to start for each grade level Pre-K through Grade 3. The key is to move between assessments until it has been determined what the child knows and can do, and what the child still needs to learn.
Pre-Kindergarten
If the child is having difficulty learning to count objects, use Assessment 1: Counting Objects.
Check the child's ability to count a small group of objects. Also, check to see if the child can “hand you” a particular number of objects taken from a larger group. Begin with smaller numbers than indicated on the assessment - begin with up to 8 objects and make the numbers smaller if necessary until the child is successful.
Kindergarten
If the child is having difficulty learning to count objects, use Assessment 1: Counting Objects.
Begin with smaller numbers than indicated in the assessment. Start with 12 objects and make the numbers smaller if necessary until the child is successful.
First Grade
If the child is having difficulty counting and/or comparing numbers, use Assessment 2: Changing Numbers.
Check to see if the child recognizes that one number is contained in another number and can change one number to another. If it becomes evident through the Changing Numbers assessment that the child is not counting with ease and facility, check his or her ability to count. Use Assessment 1: Counting Numbers.

If the child is having difficulty learning addition and subtraction facts, use Assessment 4: Number Arrangements.
If the child is not able to describe parts of numbers, check his or her understanding of the relationships between numbers by using Assessment 2: Changing Numbers.

If the child is unable to describe parts of numbers, check his or her understanding of number combinations using Assessment 5: Combination Trains and Assessment 6: Hiding Assessment.
Second and Third Grade
If the child is having difficulty learning basic addition and subtraction facts use Assessment 5: Combination Trains and Assessment 6: Hiding Assessment.
If the child counts to find the total for most of the combinations or is unable to tell the missing parts of numbers larger than 3 or 4, check the child's ability to recognize and describe parts of numbers and his or her ability to recognize small groups without counting. Use Assessment 4: Number Arrangements.

If the child is having difficulty comparing numbers or solving comparative subtraction problems, use Assessment 3: More/Less Trains.
Determine his or her level of understanding of comparing. If comparing numbers is not easy for the child, also check the child's knowledge of particular relationships between numbers by using Assessment 2: Changing Numbers.

If the child is having difficulty understanding place value concepts, use Assessment 8: Grouping Tens.
If necessary, check the child's idea of numbers as one ten and leftovers using the Going Back sections of Numbers as Tens and Ones assessment as well as Assessment 7: Ten Frames.

If the child is having trouble working with addition and subtraction of two-digit numbers, use Assessment 6: Hiding Assessment.
Check the child's knowledge of number combinations to 10. Also check the child's ability to think of numbers as composed of tens and ones by using Assessment 8: Grouping Tens. If the child can think of numbers as composed of tens and ones, check his or her ability to add and subtract teen numbers by using Assessment 7: Ten Frames. If the child can make one ten and break apart one ten with ease, check his or her ability to work with several tens and ones using Assessment 9: Two-Digit Addition and Subtraction.
Using Developing Number Concepts for Intervention
The range of instructional needs within one classroom is large. All of the Developing Number Concepts teacher-directed and independent activities are “expandable” and, therefore, help teachers differentiate their instruction to meet the range of needs in their classroom. Teachers can continually differentiate their instruction during the designated block of time for math instruction. Usually, whole group instruction is provided, and then classrooms and instruction are organized in the form of Math Stations. Math Stations are activities organized in the classroom for students to work with partners, or individually. Students frequently work at Independent Math Stations while the teacher conducts small group, differentiated, explicit instruction in a Teacher-Led Small Group setting.
How is Differentiated Instruction Implemented with Small Groups?
The teacher forms a small group based on student data from observation and the AMC assessment. The teacher determines the appropriate small group lesson based on the specific needs of the children in the group.
How is Differentiated Instruction Implemented with Independent Math Stations?
To meet their needs, it will not be necessary to provide different children with different tasks using Developing Number Concepts. Rather, each activity can be presented at a variety of levels so that most of the time children can be working side by side on different levels of a single activity.
Each of the three DNC books includes information on how teachers can meet the range of needs using the activities and lessons.
School Districts Using AMC and DNC for Intervention

Houston Independent School District, Houston, Texas
San Diego Unified School District, San Diego, California