Mathematics Assessment Work Sample - Scored Student …...The translation is adequately developed...

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Transcript of Mathematics Assessment Work Sample - Scored Student …...The translation is adequately developed...

Page 1: Mathematics Assessment Work Sample - Scored Student …...The translation is adequately developed and displayed. RS 3: The value from the linear model is not found, making the comparison
Page 2: Mathematics Assessment Work Sample - Scored Student …...The translation is adequately developed and displayed. RS 3: The value from the linear model is not found, making the comparison
Page 3: Mathematics Assessment Work Sample - Scored Student …...The translation is adequately developed and displayed. RS 3: The value from the linear model is not found, making the comparison
Page 4: Mathematics Assessment Work Sample - Scored Student …...The translation is adequately developed and displayed. RS 3: The value from the linear model is not found, making the comparison
Page 5: Mathematics Assessment Work Sample - Scored Student …...The translation is adequately developed and displayed. RS 3: The value from the linear model is not found, making the comparison
Page 6: Mathematics Assessment Work Sample - Scored Student …...The translation is adequately developed and displayed. RS 3: The value from the linear model is not found, making the comparison
Page 7: Mathematics Assessment Work Sample - Scored Student …...The translation is adequately developed and displayed. RS 3: The value from the linear model is not found, making the comparison
Page 8: Mathematics Assessment Work Sample - Scored Student …...The translation is adequately developed and displayed. RS 3: The value from the linear model is not found, making the comparison
Page 9: Mathematics Assessment Work Sample - Scored Student …...The translation is adequately developed and displayed. RS 3: The value from the linear model is not found, making the comparison
Page 10: Mathematics Assessment Work Sample - Scored Student …...The translation is adequately developed and displayed. RS 3: The value from the linear model is not found, making the comparison
Page 11: Mathematics Assessment Work Sample - Scored Student …...The translation is adequately developed and displayed. RS 3: The value from the linear model is not found, making the comparison
Page 12: Mathematics Assessment Work Sample - Scored Student …...The translation is adequately developed and displayed. RS 3: The value from the linear model is not found, making the comparison
Page 13: Mathematics Assessment Work Sample - Scored Student …...The translation is adequately developed and displayed. RS 3: The value from the linear model is not found, making the comparison

Scores and Commentary: Car Prices, Paper #A-1

Making Sense of the Task

(MS)

Representing and Solving

the Task (RS)

Communicating Reasoning

(CR)

Accuracy

(AC)

Reflecting and Evaluating

(RE)

5

6

6

5

6

MS 5: The interpretation is thoroughly developed. The student works the problem twice and checks it a third way, demonstrating evidence of a firm grasp of depreciation in this context.

RS 6: The representations used are insightful. The student uses the graphing calculator to find regression models, then completes the process by hand, choosing appropriate points that approximate the distribution. Finally, these models are used to determine if the original price from each seems reasonable, making it enhanced.

CR 6: The communication is enhanced with examples that allow the reader to move easily from one thought to another. The mathematical notation is elegant and enhances the communication.

AC 5: The solution is correct and enhanced by generalizations (comparing the original price to the model).

RE 6: The solution is justified completely by reworking the task using a different method, evaluating the relative effectiveness of different approaches. The student provides evidence of considering other interpretations (maybe the starting price makes more sense in the linear model).

Page 14: Mathematics Assessment Work Sample - Scored Student …...The translation is adequately developed and displayed. RS 3: The value from the linear model is not found, making the comparison

Scores and Commentary: Car Prices, Paper #A-21

Making Sense of the Task

(MS)

Representing and Solving

the Task (RS)

Communicating Reasoning

(CR)

Accuracy

(AC)

Reflecting and Evaluating

(RE)

3

4

4

3

4

MS 3: The interpretation of the task is partially developed. The student selects consecutive points and does not address the concept of ‘best fit’. Likewise, they do not compare the resulting line or curve to the rest of the data.

RS 4: The strategy selected is effective and complete.

CR 4: The work follows a clear and coherent path and leads to a clearly identified solution.

AC 3: Although arriving at a correct answer, the solution contains errors. In both linear functions, the majority of the data lies either above or below the model. By choosing the first two points for the exponential model, the student is taking a risk that function will not fit the rest of the data well.

RE 4: The review is complete in that it justifies the outcome (even though the flaws are not recognized).

Page 15: Mathematics Assessment Work Sample - Scored Student …...The translation is adequately developed and displayed. RS 3: The value from the linear model is not found, making the comparison

Scores and Commentary: Car Prices, Paper #A-10

Making Sense of the Task

(MS)

Representing and Solving

the Task (RS)

Communicating Reasoning

(CR)

Accuracy

(AC)

Reflecting and Evaluating

(RE)

4

3

3

3

1

MS 4: The student has a good understanding of the task and is proficient in the use of a graphing calculator. The translation is adequately developed and displayed.

RS 3: The value from the linear model is not found, making the comparison incomplete. The student does not provide a visual representation of the models to assess the fit.

CR 3: The communication of the reasoning has gaps. The only justification given for the answer is based on the correlation coefficient. The linear model is not compared beyond that argument.

AC 3: The solution is partially complete in that the linear interpretation is left unfinished.

RE 1: The review is not evident.

Page 16: Mathematics Assessment Work Sample - Scored Student …...The translation is adequately developed and displayed. RS 3: The value from the linear model is not found, making the comparison

Scores and Commentary: Car Prices, Paper #A-33

Making Sense of the Task

(MS)

Representing and Solving

the Task (RS)

Communicating Reasoning

(CR)

Accuracy

(AC)

Reflecting and Evaluating

(RE)

2

3

3

2

2

MS 2: The student uses inappropriate concepts. There is no explanation as to how outliers are determined. The student confuses exponential with quadratic.

RS 3: The strategy chosen is partially effective. The initial linear model y = -362.89x + 1859 is flawed, but the second linear model y = -362.89x + 9909 is a better representation of the data. If a quadratic model were required (and no computation errors were made) the employed method would have yielded a quadratic function.

CR 3: There are significant gaps in the reasoning. There is no explanation of the outliers and the second y-intercept of 9909.

AC 2: The solution is incomplete.

RE 2: The graph is not an effect review and the second linear equation is in unresolved conflict with the first linear equation.

Page 17: Mathematics Assessment Work Sample - Scored Student …...The translation is adequately developed and displayed. RS 3: The value from the linear model is not found, making the comparison

Scores and Commentary: Car Prices, Paper #A-30

Making Sense of the Task

(MS)

Representing and Solving

the Task (RS)

Communicating Reasoning

(CR)

Accuracy

(AC)

Reflecting and Evaluating

(RE)

2

1

2

1

1

MS 2: The interpretation is sketchy. The student tries a variety of translations but none are successful. The slope computation m = -369.6 is the only useful computation.

RS 1: There is no clear strategy evident. The student really does not know what to do.

CR 2: There is communication present but it is underdeveloped or inappropriate.

AC 1: No solution is present, making it both incorrect and incomplete.

RE 1: No review is evident.