Evaluating Student Learning
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Grading in CMP 2
Examples of Grading Systems
Comments on Partner Quizzes
Examples of Evaluating Specific Assessment Pieces
Grading in CMP 2
The multidimensional assessment in Connected Mathematics provides opportunities to collect broad and rich information about students' knowledge. Teachers face the challenge of converting some of this information into a grade to communicate a level of achievement to both students and parents. The following assessment items offer teachers an opportunity to assign grades: ACE exercises, Check-Ups, Quizzes, Mathematical Reflections, Looking Back and Looking Ahead (Unit Reviews) Unit Tests, Projects, notebooks, and Self- Assessments. The use of these assessments for grading and the value assigned to them vary from teacher to teacher. While most teachers view the problems as the time to learn and practice mathematical concepts and skills, some teachers will occasionally assign a grade to a problem. Some teachers also choose to grade class participation.
Examples of Grading Systems
Two teachers' grading schemes for their CMP mathematics classes follow. These are given as examples of possible grading schemes. Note that each of these teachers has made independent decisions about how best to use the assessment tools in CMP for grading purposes.
Example 1: Ms. Jones
I try to take several things into account when grading students in mathematics class. I work to build a learning community where everyone feels free to voice his or her thoughts so that we can make sense of the mathematics together. I try very hard to assess and grade only those things that we value in the classroom.
Participation
Because participating in discussions and activities is so important in helping the students make sense of the mathematics, this is one part of the students' grades. They rate themselves at the end of each week on how well they participated throughout the week. Below is a sample of the grading sheet they fill out. The participation grade counts as 15% of their total mathematics grade.
Participation Grading Sheet
Name____________________________________________
Week of __________________________________________
We have completed almost a full week of math class. Think about how well you participated in class this week.
Answer the following questions, as they will help you give yourself a fair participation grade for this week.
Did you participate in the discussions?
Did you come prepared to class, having done your homework, so that you could ask questions?
Did you ask questions when you didn't understand?
Did you LISTEN carefully to others?
Now count your "yes" responses.
If you answered "yes" to ALL of them, HOORAY for you! You are doing a great job. Give yourself a 5.
If you answered "yes" to most of them, give yourself a 4.
If you answered "yes" to a couple of them, give yourself a 3.
If you answered "no" to several of these, give yourself a 2, and rethink your role in this class or talk to your teacher.
I grade myself a _____ for this week. Signature ____________________
Journal
Ideas become clear when we talk about them and when we write about them. Because I feel it is very important to be able to communicate mathematically in writing, students' journals also figure into their grade. We use the journals for problem solving, communicating what they do and do not understand, and reflecting on each Investigation to summarize the ideas. I try to collect them at least once every two weeks so I remain in constant communication with each student. The journal grade counts as 15% of their total grade.
Journal Grading Sheet
You will earn a "5" if:
You effectively communicate your thoughts.
You use appropriate vocabulary.
You use a variety of strategies to solve problems.
You write as if you are talking about mathematics.
Your journal is well organized, and entries are labeled and dated.
You will earn a "4" if:
You are effective in communicating your thoughts most of the time.
You use some appropriate vocabulary.
You use some different strategies when solving problems.
Your journal is fairly well organized, and most entries are labeled and dated.
You will earn a "3" if:
You attempt to communicate your thoughts but your entries are hard to follow at times; be sure to write ALL that you know.
You use some appropriate vocabulary but need to use more.
You need to work on using a variety of strategies to solve problems.
Your journal is not organized with the entries labeled and dated.
If you earn a "2"
Please see me.
Date graded Grade Received
____________________________ _____________
____________________________ _____________
____________________________ _____________
Homework
The curriculum is problem centered. This means that the students will investigate mathematical ideas within the context of a realistic problem, as opposed to looking only at numbers. Students spend much of each class period working with a partner or in a small group trying to make sense of a problem. We then summarize the investigation with a whole class discussion. The ACE exercises assigned offer students an opportunity to practice those ideas alone and to think about them in more depth. Homework assignments are very important! They provide students the opportunity to assess their own understanding. They then can bring their insight and/or questions with them to class the next day. We usually start each class period going over the exercises that caused difficulty or that students just wanted to discuss. Keeping up with the homework (given about 3 or 4 times a week) helps students to stay on top of their learning. It also allows me to see what students are struggling with and making sense of. Homework assignment grades count as 20% of their total grade.
Partner Quizzes
All of the quizzes from CMP are done with a partner. Because a lot of what we do in class is done with others, I want to assess students "putting their heads together," as well. Again, I try to grade what I value, which is working together. Quiz grades count as 20% of their total grade.
Final Assessment
At the end of each unit an individual assessment is given. Sometimes it is a written test, sometimes a project, and sometimes a writing assignment. These serve as an opportunity for students to show what they, as individuals, have learned from the whole unit. Test/project grades count as 30% of their total grade, as they are a culmination of the whole unit.
Grading Summary:
Participation . . . . . . 15%
Journals . . . . . . . . . . . 15%
Homework . . . . . . . . 20%
Partner Quizzes . . . . 20%
Tests/Projects . . . . . . 30%
Example 2: Mr. Smith
Journals (Part of the Notebook)
Collect student journals once a week.
Scoring Rubric for Journals
5 Work for all Investigation problems (done in class, to date) and Reflections (well labeled and easy to find/follow)
4 Most class work and Reflections (well labeled and easy to find/follow)
3 Some missing class work or Reflections (not well labeled or easy to find/follow)
Below a 3 is not acceptable. Students have to come in at lunch or after school and meet with me and work on their journal until it is at least level 3.
Participation
Participation means questioning, listening, and offering ideas. Students are given a participation grading sheet every Monday, to be handed in on Friday. Students fill these out throughout the week, giving evidence of their participation in the class. On the sheets they are to note when and how they contribute to class discussion and when they use an idea from class discussion to revise their work or their thinking.
Scoring Rubric for Participation
5 Student has made an extra effort to participate and help others in the class to understand the mathematics. Student gave evidence of participating all 5 days of the week.
4 Student made an effort to participate, giving evidence of at least 4 days of participation for the week.
3 Student made some effort to participate, giving evidence of at least 3 days of class participation for the week.
Below a 3 is not acceptable. I talk with student about his or her lack of effort. If no improvement is seen in the next week, a parent or guardian is called and informed of the problem.
Homework (selected ACE exercises)
In class, before homework is checked or collected, students are given the opportunity to ask questions about the assignment. I do not give answers or tell how to solve the exercise but, with the class's help, work with students to help them understand what the exercise is asking. Students have the right to revise any of their work while this conversation is going on and not be marked down. Grading is strict on this work because students have the opportunity to take care of it themselves and get help.
Scoring Rubric for Homework
✓ + Close to perfect
✓ All problems attempted, most work done correctly
✓ - Most problems attempted, some given answers wrong or incomplete
✓ -- Not much work, most work wrong or incomplete
0 No work
Projects
A 6-point holistic rubric is used for all projects
Scoring Rubric for Projects
5 Project is complete, mathematics is correct, work is neat and easy to follow.
4 Project is mostly complete, most of the mathematics is correct, work is neat and easy enough to follow.
3 Project has some missing pieces, some of the mathematics is correct, work takes some effort by the teacher to follow.
2 Project is missing some major parts, there are several problems with the mathematics, it takes extra effort for the teacher to follow the work.
1 Project shows little to no significant work.
0 No project is submitted.
Check-Ups, Partner Quizzes, and Unit Tests
With partner quizzes, only the revised paper (the one turned in the second time) is scored for a grade.
Scoring Rubric for Check-Ups, Partner Quizzes, and Unit Tests
Each assessment has its own point-marking scheme devised by me. Points are determined by the amount of work asked for to solve each problem. Not all problems are awarded the same number of points.
Assigning grades to numbers and checks
✓ + or 5's = A
✓ or 4's = B
✓ - or 3's = C
✓ -- or 2's = D
1's and 0's = E
Comments on Partner Quizzes
The quizzes provided in the Connected Mathematics assessment package are a feature unique to the curriculum. The assumptions under which the quizzes were created present a unique management and grading situation for teachers.
Students work in pairs.
Students are permitted to use their notebooks, calculators, and any other appropriate materials.
Pairs submit a draft of the quiz for teacher input, revise their work, and turn in the finished product for assessment.
Partner quizzes are designed to be completed by students working in pairs. There are several ways to choose student pairs for a quiz. Most teachers use one or more of the following:
Students choose their own partners.
Partners are chosen in some random way.
The teacher picks the pairs to work together.
Seating assignment determines partners. Many teachers keep track of who works with whom and have a rule that you cannot have the same partner twice until you have been paired with everyone in the class at least once.
It is assumed that each pair of students will have one opportunity to revise their work on the quiz based on teacher feedback before submitting it for a grade. When a pair has completed the quiz, they can submit separate papers or one paper with both names on it.
Giving feedback generally involves telling students which questions they have answered incorrectly or how many of the possible points they would receive for a question. It should be seen as an opportunity to let students know if they are on track or if they need to rethink a problem. Giving feedback should not mean reteaching or leading students to the correct solution. Here are some methods Connected Mathematics teachers have used for giving feedback to students.
Check the quizzes and write the number of points achieved next to each question. Then, allow the pair to revise all the questions.
Check the quizzes and write the number of points achieved next to each question. Then, allow the pair to revise one question of their choice. (If they write in a different color, you need to check only the new information.)
While students take the quiz, allow each pair to confer with you once about one problem.
Allowing students to revise their work is a new concept for many mathematics teachers. If you have never done this before, you might ask one of the language-arts teachers in your school how he or she orchestrates revision work for student writing, since this is a common practice in that discipline.
Quiz questions are richer and more challenging than Check-up questions. The tasks on quizzes encourage collaboration and reflect the kind of learning that occurs during class. These questions provide insight into how students apply the ideas from the unit to new situations. The nature of the partner quizzes provides a grading situation in which rubrics can assist in the evaluation of the students' knowledge.
Examples of Evaluating Specific Assessment Pieces
Grade 6
Bits and Pieces I Modified Checkup
A Guide as to how to adjust a check up to include all students
Student work
Teacher Comments
Grade 7
Streatching and Shrinking Self Assessment
Moving Straight Ahead Check-up and Quiz
Accentuate the Negative Unit Vocabulary
Grade 8
Looking for Pythagoras Self Assessment
Frogs and Fleas Unit Vocabulary
Say it with Symbols Check up
You may want to investigate other resources for aid in establishing scoring rubrics for these types of assessment. Some examples are: Alternative Assessment in Mathematics from the EQUALS project; Mathematics Assessment -Myths, Models, Good Questions and Practical Suggestions from NCTM; and the Balanced Assessment Project from Dale Seymour Publications.