MTE 494 Chapter 6: Assessments in Mathematics by Andie Jia

1.1 What is a diagnostic assessment?

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Diagnostic assessments usually consist of open-ended questions to gauge students' command of prior knowledge. Questions on diagnostic assessments evaluate students' conceptual understanding rather than their ability to perform algebraic manipulations.

1.2 Quick Write Activity

mjia17 — 2023-11-11 21:08:31 UTC

Besides letting students fill out a questionnaire (such as a Google Form) as the diagnostic assessment, teachers can also supply students with pieces of scratch paper for the quick write task. For example, the Quick Write Activity (QWA) should include questions like:

What is a parallelogram?
Explain the relationship between a parallelogram, a rectangle, and a square.
How do you prove a given quadrilateral is a square or rhombus?

To minimize unnecessary stress, QWA is not graded. If I include those QWAs in students' grade calculations, students might feel overwhelmed and shifted their focus on how to develop their response strategically for high grades.

1.3 Simple Computational Questions

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Sometimes doing QWA can be time-consuming, so a few (1-2) simple questions are excellent replacements. Those questions are not necessarily challenging, but they are a good way for teachers to see how students have approached the problem. However, teachers must ensure that all questions are level-appropriate, which means if the class is Geometry, questions that cover Algebra 2/Precalculus content should not be given.

2.1 Visible Thinking Routines

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Assessment in mathematics classrooms does not always have to be in paper-and-pencil format. Sometimes collaborative assessment allows room for constructive feedback. There are multiple ways to exercise the Visible Thinking Routine (VTR) strategy.

Two Stars and a Wish (TSW): Rather than evaluating peers' work based on a rubric. TSW allows students and teachers to give written constructive feedback on the area of refinement and the area of reinforcement.
The KWL Chart: Is recommended to be used as a form of in-class participation. Students will complete the K (Know) and W (Will Know) sections at the beginning of the lesson. Toward the end of the lesson, students will complete the L (Learned) section of the KWL Chart. I utilize the Pass/Fail grading for all KWL participation assignments. Again, to give my students those easy points.
Three Do's and Three Don'ts (TDTD): This activity gives me and my students opportunities to reflect (teaching strategies for me and learning strategies for my students). For example, students can share tips on how to avoid repeating the same mistakes in the future or how to avoid silly computational errors in easy-level questions.

2.2 Think Pair Share (TPS)

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This interactive activity emphasizes students' ability to speak and collaborate with peers, which may sound intimidating to students who are non-native speakers and quiet learners. However, students will lose the precious opportunity to improve if they do not complete the TPS activity. To encourage active participation, students will receive full credit for completing the TPS of the day.

2.3 The Double Bubble Map

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The Double Bubble Map (DBM), or the DSD Chart (DSD stands for Differences, Similarities, and Differences), replaces the Venn Diagram but preserves the function of organizing ideas and concepts. The DSD Chart is especially helpful for Geometry, when learning about the congruence of triangles and the properties of parallelograms.

Sample DSD Chart: Parallelogram vs. Quadrilateral

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Students can fill up the nine empty bubbles as the evidence of learning and participation.

3.1 Agree, Disagree, and Depend (ADND)

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The ADND task requires students to justify their choice of answer; that is, they must formulate an argument to explain why the given statement is correct, incorrect, or holds under certain circumstances. For example, the question above, which is provided by ETS, asks the test-taker to compare the quantities.

Note that the question comes from the Sample GRE Quantitative Reasoning Questions, which means high schoolers won't see it on the SAT or ACT Test. But that does not mean they do not need any mathematical reasoning skills.

Students who selected A assume that QS is the altitude of the triangle QPR from the vertex Q to the side PR. The question does not specify whether QS is perpendicular to PR.

Students who selected C assume that S is the midpoint of PR since the graph looks like it. Does the question mention that QS is the median of PR? If not, then C is not the correct answer.

For students who think D is the correct answer, they need to justify their answers with counterexamples. That is, by specifying that S is not a fixed point on PR.

3.2 Standard-Based Grading

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The test score from a randomly designed exam gives students ambiguous feedback on their academic performance. Indeed, a 27/40 on an exam translates to a D+, but the grade of D+ is a misrepresentation for students who correctly answered all the basic- and intermediate-level questions. Instead, I will design my exams with three rigor levels:

Basic Level: Does not require any cognitive skills beyond rote memorization. Can be solved without a calculator.
Intermediate Level: Requires a basic grasp of the concept but does not expect extended thinking or proof-writing.
Hard Level: Requires multi-step problem-solving and reasoning skills. Students cannot correctly answer the question with just a calculator.

Letter Grades Assignment:

D (65): cannot correctly answer at least half of the basic-level questions.
C (75): answers at least half of the basic-level questions correctly.
C+ (78): answers all the basic-level questions correctly.
B- (82): answers less than half of the intermediate-level questions and all the basic-level questions correctly.
B (85): answers at least half of the intermediate-level questions and all the basic-level questions correctly.
B+ (88): answers all basic- and intermediate-level questions correctly.
A- (92): answers a few hard-level questions correctly in addition to the criteria for a grade of B+.
A (100): answers some hard-level questions correctly in addition to the criteria for a grade of B+.

The SBG allows me to give unambiguous feedback and students shall receive reasonable grades for their level of mastery.

3.3 Self-Evaluation

mjia17 — 2023-11-12 00:36:28 UTC

Students can always evaluate themselves on any assessment instead of one from a teacher. Grades from self-evaluation usually accurately represent students' level of mastery because students know themselves better than teachers in most cases.

Strategies to Maximize the Use of Self-Assessment

mjia17 — 2023-11-12 00:39:16 UTC