Identify and Write Fractions: Representational Level

More Teaching Plans on this topic: Concrete

PHASE 3: Evaluation

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
Timer (for writing fractions)

Student –

Appropriate response sheet/curriculum slice/probe
Graph/chart

Description:

You should evaluate both the students’ abilities to draw fractional parts and to write fractional parts. The following steps outline a process for doing this for both skills. It is suggested that you evaluate students’ ability to draw fractional parts first since this is what you will be teaching first and providing student practice for first. When students show mastery drawing fractional parts, then you will teach writing fractions. At this point you will evaluate your students’ progress in writing fractions.

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.

For drawing fractional parts, an appropriate number of tasks to indicate proficiency is 8 to 10 tasks. This number range allows you to complete the evaluation period within 3 to 5 minutes. *It is important that this evaluation strategy is time-efficient because it should be done every day or every other day and if it is not time-efficient, you will probably not implement this important evaluation strategy.
For evaluating writing fractions, provide at least 20 prompts. Then time students as they respond to the prompts for one minute. Since writing fractions is an “abstract level” task, it is important to use rate/fluency to measure mastery, not only accuracy. Writing fractions efficiently will allow students to be more successful as they work with more advanced math concepts/skills that will involve writing and using fractions.

3) Provide appropriate number of prompts in an appropriate format so students can respond.

For drawing fractional parts, 8-10 prompts on a curriculum slice/probe that reflect the range of skills you want to evaluate (e.g. one or more fractional parts and using one or more fraction models.) is appropriate.
For writing fractions, provide 20 or more prompts on a curriculum slice/probe that reflect the range of skills you want to evaluate (e.g. one or more fractional parts and using one or more fraction models) is appropriate.
Based on the skill, your students’ learning characteristics, and your preference, the curriculum slice or probe could be written in nature (e.g. a sheet with appropriate prompts; index cards with appropriate prompts), or oral in nature with visual cues (e.g. say, “show me ‘one-half’ by drawing,” or, “write the fraction that means ‘one-half’” while holding up a card with “one-half” written on it.), or a combination of written curriculum slices/probes and oral prompts with visual cues (e.g. students have a curriculum slice/probe that is numbered “1, 2, 3…” where each number has several fractional parts written – “one-half,” “one-eighth,” “one-fourth,” and students circle the correct response (drawing or writing the appropriate fractional part) when demonstrated by the teacher with a drawing.

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

5) Give directions.

6) Conduct evaluation.

7) Count corrects and incorrects (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 that represents the proficiency (for drawing fractional parts, this should be 100% – 8 out of 8 corrects or 10 out of 10 corrects; for writing fractions, this should be at least 20 with no more than two incorrects) should be visible on each students’ graph/chart.

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:

Representational Level: demonstrates 100% accuracy drawing fractional parts (given 8-10 response tasks) over two to three consecutive days.

Abstract Level: demonstrates near 100% accuracy for writing fractions given drawings and language that describes fractional parts (two or fewer incorrects) 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.

Assessment

Purpose: to evaluate student conceptual understanding and provide you information to plan additional instruction.

Flexible Math Interview

Description:

During small group time, the teacher will encourage students to draw fractions and write fractions, then have students describe what they represent. The teacher notes particular misunderstanding/non-understanding for individual students and provides additional modeling based on individual student needs.