IMP Year One Scoring Guides for Students and Teachers Introduction
The IMP Year One Scoring Guide for Students and Teachers contains individual scoring guides (rubrics) for the Problems of the Week, (POW’s) and Portfolios assigned in Year One of the Interactive Mathematics Program, (IMP). In addition, it also contains the scoring guides for all homeworks contained in Patterns, the first unit of Year One.
All POW scoring guides are based upon the Standard POW Write-Up (p. 10-11) found in The Interactive Mathematics Program Year One student textbook and Interactive Mathematics Teachers Guide for Patterns Teacher’s Guide (P. 27-28.) Although there is a standard POW Write-Up, not all POW’s use the same format or will use all the categories. These scoring guides were designed to keep the Write-Ups as consistent as possible, yet still follow the required format given in the text.
The scoring guides for the Portfolios were modeled after the POW scoring guides. The scoring guides specifically address what is required for each unit portfolio and how it should be presented. All Portfolio scoring guides have three sections. The first two sections are the same (Cover Letter and Selecting Papers), while the third section varies according to the unit.
The Complete Scoring Guides for homework assessments are to be used by students to understand the expectations of the homework and then self-assess their work. The teacher will use the General Homework Scoring Guide to evaluate each homework. The teacher scoring guide is based on a holistic scoring approach using a 0-5 scale for each assignment. Of course, the teacher can use the complete scoring guide in their assessment – but a holistic approach will be most practical and specific comments can be addressed as needed. Students should use the scoring guide to help complete the homework, and then self-assess their work during the homework review. This allows the student to be familiar with the scoring guide, make corrections as needed, and then select appropriate scoring guide values for their work.
Aligning Teacher and Student Expectations
One of the most challenging tasks of the new math reform is getting students to understand what is expected of them in all of their work. For the most part, students want to do work that is appropriate and will earn them good grades. However, students will sometimes produce work that misses the point or is incomplete. In many cases the students simply did not understand the wording of the questions(s), are unclear of specifically what was being asked for, or understand how to write an answer that explains their work -- especially if they do not get the right answer or finish the problem.
The math reform has also changed both the student and teacher’s perspective of what math is, how math is taught, and most importantly, how to maintain and utilize our math knowledge in the real world. Now our students are now being asked to do work outside of the traditional scope of mathematics. They also have part of their math grade reflect these “nonmathematical activities,” such as writing, oral reports, and even artistic representations. Therefore, it is critical that students clearly understand what is expected of them and how to present it so they can be as successful as possible in their work. In addition, this “upfront policy” of providing what is expected helps to develop students that have an internal model of how to be successful.
Uniform Standards for Teachers
One of the greatest concerns of implementing any large-scale problem-based learning model is that there must be consistency in how all of our teachers assess their students. And this is especially true for entering ninth grade students, as this will set the tone of the next four years. If all teachers can consistently assess student work with the same standards, it sends a clear message to students that there are performance levels at which they must achieve, regardless of the teacher or the school. Consistency in assessment allows students to achieve proficiency in using a scoring model, expanding the model, and then creating their own self-assessment models.
Maximizing Student Outcomes
Student outcomes are most often a direct reflection of how well students understand the teacher’s expectations and their ability to address these expectations. Traditionally, outcomes were based upon the ability to simply provide correct answers. However, our new standards now require assessment outcomes to include writing and communicating mathematical ideas and concepts, as well as developing and applying problem solving skills. Therefore, to maximize student outcomes there must be clear models of satisfactory work as well as a scoring guide that reflects the required elements of the work. And since this now reflects of new model of learning for students, time needs to be allotted for student growth in the various performance outcomes. For many students, specifically writing to a topic, explaining a thought process, or describing how they got “unstuck” is a challenge that will take considerable time to develop proficiently.
Learning is a process that requires students to produce specific pieces of work to demonstrate their proficiency in various performance standards. However, it is equally important that students learn to evaluate their own work. By evaluating their own work, students now accept responsibility for not only completing the work but share the responsibility of assessing it. Generally, students learn just as much from the assessment of the work as they do from the task of doing the work itself. In addition, this often motivates students to “go back” and complete weak sections or expand sections in which they have a degree of expertise. As students become proficient at assessing their own work they gradually accept the role of being their own teacher. And in an ideal educational experience, the teacher now becomes the mentor that asks students to reflect further on their internal models and problem solving skills.
Ideally, students will not only self-assess their own work they will also assess other students’ work. By experiencing other student ideas and methods, students often see ways in which they could improve their work.
Scoring Guide Instructions
Scoring Guides for POW’s and Portfolios should be given to students in advance so that they understand the expectations of each assignment.
Scoring guides for each POW and Portfolio have a single page scoring table. When students hand in their POW’s and Portfolios they should staple the COMPLETED scoring table as the top page of the assignment. The teacher will then check the student evaluation to make the necessary scoring modifications and to add any necessary comments regarding the assignment on the same scoring sheet.
Point values are assigned for each scoring criterion, for example a criterion may be worth 4 points. In order for the students to understand how to get the maximum number of points, examples of point values are given. In many examples, the full range of point values with the required information are given, for example: for our 4 point scoring criterion has all the required information for point values: 0, 1, 2, 3, and 4 (see example below).
Scoring Criterion Example: Describe why a solution is correct
0 – No description provided
1 – A poor, vague, or incomplete description of why the solution is correct with no
examples used for support
2 – A limited description of why the solution is correct with 1 general example used for
3 – A satisfactory description of why the solution is correct with at least two
examples used for support
4 – A detailed description of why the solution is correct with many specific and
and appropriate examples used for support
However, teachers should not feel restricted to using only the specific point values (0, 1, 2, 3, and 4). If a teacher feels an answer is in between two values (for example 3 and 4), the teacher has the option of going to the lower value (3) as all the required information was not supplied to receive the higher point value (4). Or, the teacher may use an intermediate value (3.5) indicating that it give more required information then the lower value specified, but did not give all the required information of the higher value. In addition, there may be times that the point values do not address every possible student outcome. Therefore, the teacher must decide which of the listed point values has required information that would be of roughly equal value. For example, a student might be asked to describe different possible answers for a solution. And the student describes all 5 the possible solutions, but all the solutions are vague and incomplete. The scoring guide gives one point for each correct description. Yet, the teacher may decide to only give 3 points since all the solutions were poorly described.
In some cases the scoring guide does not provide all the possible point values for a scoring criterion. For example a 4-point criterion may only have point values and required information for 0, 1, 2, and 4. This is purposely done so that teachers can use discretion in terms of what they consider to be “good” or “excellent” or “complete” and “extensive”. In addition, it doesn’t give students the misconception that exceptional work is worth only one point more then good work. Therefore, students may feel more inclined to put in the extra time to give quality responses for each assessment criterion.
When students hand in their POW’s they may not have the correct answers or solutions for the specific problem(s). Therefore, it will not be possible for students to provide self-assessment for correct solutions and answers since they do not know them. Students should be instructed to leave these areas blank on their scoring guide table.
Student Work Formats
Student work should use same headings and numbering system as the scoring guide so that they can easily assess their work and use the scoring tables to report the assessment values.