Rounding to Nearest 10 or 100: Abstract Level

More Teaching Plans on this topic: Concrete, Representational

PHASE 3: Evaluation

Monitor/Chart Performance

Purpose: to provide you with continuous data for evaluating student learning and whether your instruction is effective. It also provides students a visual way to “see” their learning.

Materials:

Teacher -

• Appropriate prompts if they will be oral prompts
• Appropriate visual cues when prompting orally

Student –

• Appropriate response sheet/curriculum slice/probe
• Graph/chart

Description:

Steps for Conducting Continuous Monitoring and Charting of Student Performance:

1) Choose whether students should be evaluated at the receptive/recognition level or the expressive level.

2) Choose an appropriate criteria to indicate mastery.

3) Provide appropriate number of prompts in an appropriate format (receptive/recognition or expressive) so students can respond.

At the abstract level of understanding, the most efficient format for a curriculum slice/probe is written (e.g. student responds in writing to written prompts). In some cases, you may want to use oral prompts where written examples are provided on the chalkboard/dry-erase board or overhead projector (e.g. three digit numbers written above various number lines and students respond to several teacher questions about each example: “What is the nearest ten? What is the nearest hundred? How many ones did you count on to the greatest ten? How many tens did you count back to the lesser hundred?).

4) Distribute to students the curriculum slice/probe/response sheet/concrete materials.

5) Give directions.

6) Conduct evaluation.

7) Count corrects and incorrects/mistakes (you and/or students can do this depending on the type of curriculum slice/probe used – see step #3).

8) You and/or students plot their scores on a suitable graph/chart. A goal line should be visible on each students’ graph/chart that represents the proficiency (near 100% accuracy with two or fewer incorrects/mistakes) and a rate (# of corrects per minute) that will allow them to be successful when using that skill to solve real-life problems and when using the skill for higher level mathematics that require use of that skill.

9) Discuss with children their progress as it relates to the goal line and their previous performance. Prompt them to self-evaluate.

10) Evaluate whether student(s) is ready to move to the next level of understanding or has mastered the skill at the abstract level using the following guide:

Abstract Level: demonstrates near 100% accuracy (two or fewer incorrects/mistakes) and a rate (# of corrects per minute) that will allow them to be successful when using that skill to solve real-life problems and when using the skill for higher level mathematics that require use of that skill.

11) Determine whether you need to alter or modify your instruction based on student performance.

*This assessment activity can be used with students who demonstrate difficulty with rounding at the abstract level.

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Assessment

A. Flexible Math Interview/C-R-A Assessment

Purpose: to assess where student understanding of the rounding process is “breaking down.”

Materials:

Teacher -

• Appropriate concrete materials for rounding (See Concrete Level Instructional Plan – Explicit Teacher Modeling.).
• Number lines for rounding to nearest ten or hundred.
• Appropriate examples for assessment (nearest ten and nearest hundred)
• Paper to record notes.

Description:

Have students round to the nearest ten and hundred using concrete materials, by drawing, and without concrete materials or drawings. Also have students round with and without the use of number lines. Ask students to explain their answers as they respond. Note where in the rounding process students “break down;” both at what level they begin having difficulty and at what point within that level of understanding they demonstrate misunderstanding/non-understanding. Based on where students demonstrate difficulty, provide explicit teacher modeling at that level of understanding and for the particular sub-skill they are having difficulty with. As the student demonstrates understanding, scaffold your instruction until they are ready to practice the skill independently. As students demonstrate mastery of the skill at that level of understanding, then provide explicit teacher modeling at the next level of understanding. Follow this process until students demonstrate mastery at the abstract level.

Key Ideas

Students who demonstrate difficulty at the abstract level of understanding may have “gaps” in their understanding that can trace back to the representational/drawing level or even the concrete level. By providing additional teacher modeling at the level their “gap” in understanding began and then moving them from a concrete-to-representational-to-abstract level of understanding, you can assist students to become successful at the abstract level of understanding.

Sometimes students demonstrate difficulty at the abstract level because they did not receive enough practice opportunities at the concrete and representational/drawing levels. The drawing level is a very important step for these students. Some students need continued practice drawing solutions and associating their drawings to the abstract symbols and the mental processes necessary to perform at the abstract level.

Some students understand the concept, but have difficulty remembering the steps involved to perform the skill at the abstract level. Providing students with cues they can refer to as they practice at the representational/drawing and abstract levels of instruction is very helpful. Such cueing provides them the independence to practice. Multiple practice opportunities translate into repetition and repetition enhances memory.

*See suggestions described under this section for both the concrete and representational level instructional plans.

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