criteria for math presentation

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Course info, instructors.

• Prof. Haynes Miller
• Dr. Nat Stapleton
• Saul Glasman

Departments

• Mathematics

As Taught In

Learning resource types, project laboratory in mathematics, presentations.

Next: Practice and Feedback »

In this section, Prof. Haynes Miller and Susan Ruff describe the criteria for presentations and the components of the presentation workshop.

Criteria for Good Presentations

Effective presentations provide motivation, communicate intuition, and stimulate interest, all while being mathematically accurate and informative. As is true with their experience with mathematical writing, many students do not enter the course in possession of the tools to do much more than present the facts. For example, students often come to practice presentations with the mistaken belief that a mathematical presentation must be extremely formal throughout, every term must be rigorously defined, all facts must be proven, and pictures are too infantile for this level of presentation. We try to counter these preconceptions and urge flexibility and a sense of appropriateness: sometimes things need to be presented rigorously and formally, but sometimes a picture, conceptual explanation, or example is much more effective.

Characteristics of an Effective Undergraduate Research Talk (PDF)

Presentation Workshop

For the presentation workshop, which typically lasts 50 to 80 minutes, we begin by having the two co-instructors each give a short mock presentation. These presentations are designed to address common student misconceptions about mathematics presentations. For example, to help students realize that presentations should not be relentlessly formal, the first presentation might be good in every way except that it is dull and difficult to follow because it is unnecessarily formal throughout. In contrast, the second presentation might cover the same material but use examples and figures to introduce some concepts informally, while reserving rigorous formality as a strategy for clarifying and solidifying the most subtle or important concepts.

To help students recognize the value of the second presentation relative to the first, after each presentation we ask the students a question designed to check their understanding of the content. The goal is to allow students to discover their natural tendency to overlook weaknesses in presentations. When they try to answer questions about it, they may discover that they got less from it than they had thought. The second presentation is then intended to offer a more understandable approach to the same material. Of course it’s the second time students will have heard this material, so they will naturally understand it better. But this serves a pedagogical purpose too, as it reinforces our point.

We follow the presentations with a class discussion on how to give a good presentation. Carefully designing two mock presentations has the virtue of drawing attention to key learning objectives, but doing so is challenging. In Spring 2013, each mock presentation was delivered by a different instructor and so had different advantages and disadvantages, as is stressed by Haynes’ comments on the workshop (PDF) . In the past we have reduced accidental differences between the presentations by having a single instructor present both, and we may return to that approach in the future.

After the mock presentations, the class discusses the characteristics of a good presentation. Questions we discuss often include the following:

• What are the reasons to include a proof in a presentation?
• What other strategies are available for achieving these goals?
• What strategies can be used to make a math presentation engaging for the target audience of math majors?

In Spring 2013, the mock presentations ran long, and the class session was shorter than we had originally planned because of scheduling disruptions at MIT. Thus, the subsequent discussion was rushed. The presentation workshop works best when there is ample time for discussion.

We hope that students come away from this workshop with an appreciation for some of the complexities in designing a good presentation. Pretty much every choice involved has both pros and cons.

• Download video

This video features the presentation workshop from Spring 2013. The co-instructors deliver mock presentations, which are followed by a brief class discussion comparing the two presentations.

Chalk Talks versus Slide Presentations

Different instructors have set different expectations for the presentations. Some have insisted on slide presentations. More typically, students are encouraged to use media suited to the demands of the presentation.

When discussing slide presentations in mathematics, we usually make the following points:

• When slides contain large amounts of text (or equations), the audience cannot read and listen at the same time, so strategies are needed either to reduce the content on the slides or to guide the audience through the content.
• The audience needs time to absorb math concepts, but it is very easy to click through slides too quickly, especially when the presenter is nervous, so strategies are needed to give the audience time to think.
• The audience cannot refer to past slides to remind themselves of the meaning of new notation or of the purpose of details being presented, so strategies are needed to help the audience remember important points.

A Note about Scheduling

In the course, roughly one group presents each week. Experience has shown that the first team to present sets the bar for the rest of the semester. It is important that the first team be chosen carefully and be guided well so that they give a strong presentation.

« Previous: Presentations | Next: Sample Student Presentation »

In this section, Prof. Haynes Miller and Susan Ruff explain their use of practice presentations as well as how teams receive feedback on their presentations from both faculty and peers.

Students present informally during the mentor meetings and debriefings. When it is a team’s turn to present formally to the class, they first prepare by practicing with the help of their mentor for that project, the communication instructor, and the lead instructor. After the formal presentation to the class, the team receives completed feedback forms from peers and from the course staff.

Practice Presentations

Each presentation is preceded by a practice presentation three to five days before the in-class presentation.

Students are told to treat the practice presentation as though it were the final presentation. This encourages students to prepare appropriately. Practice presentations are typically attended by the group’s mentor for that project, the communication instructor, and the lead instructor. We schedule two hours for each practice session to allow ample time both for the one-hour presentation and for feedback and discussion.

Feedback on Practice Presentations

Students share the work of presenting in various ways. In Spring 2013, all teams gave presentations in which one student talked for the first third, another for the next third, and another for the final third. During the practice presentations, we would stop after each student’s part, and the whole group would discuss what we saw. Practice presentations were typically on Fridays, with the final in-class presentation happening on the subsequent Monday. The students would do a lot of work over the weekend. We were very pleased with how well the students picked up both the letter and the spirit of our critiques and put them into their final presentations. We loved doing the practice presentations with the students, helping them improve their presentations, and seeing the improvement from the practice to the final presentation in the class.

Typically Susan would write comments as the practice presentation progressed, and then give these comments to the students at the end of the practice presentation.

Alternatives

Over the years, instructors have approached practice presentations and final presentations in different ways. Here are some variations that have been tried:

• A mini conference at the end of the semester. One year, we concentrated all the talks into a mini “conference” at the end of the term. One disadvantage was that students couldn’t learn from their classmates’ talks in time to improve their own. Another was that because the whole class only met together for the start-of-term workshops and for presentations, the class did not meet as a whole group for most of the semester, and the students didn’t really interact with any classmates other than those in their teams.
• Slide-based talks. It can be challenging to get students to put adequate effort into a presentation, especially if it is a chalk and blackboard talk. One semester, we insisted on slide presentations, which forced students to do a certain amount of preparation and improved the overall quality of presentations. This puts a burden of learning the slide presentation technology (often Beamer) on students, and does not reflect current practice in many areas of mathematics.
• Give practice presentation comments after the whole group has presented. In the past, we sometimes had the entire team give the presentation before giving feedback, rather than after each person presented his or her part. This allowed us to see the transitions and overall structure of the presentation before formulating comments. The converse practice, of interrupting presentations repeatedly for comments, does not work well; it is discouraging, it fails to let students get into the swing of their presentation, and students do not have the chance to absorb suggestions.

Peer Feedback

In Spring 2013, students were asked to give written feedback on their classmates’ presentations.

Students made comments in the following categories:

• What did you particularly like about the presentation?
• Which part of the presentation was most difficult to follow?
• What advice do you have for the presenters for the future?

The students had the option of signing the response form on the front, if they were willing to let others see their names attached to their comments, or they could sign the form on the back, if they didn’t want their names attached to their comments. At the end of class, we collected these sheets, scanned the fronts, sent them to the presenters, and posted them on the course website. Most students chose to have their name visible, and the comments were generally quite constructive and astute. We do not have quantitative evidence on the impact of these forms, but we had the feeling that they helped students be more engaged in their classmates’ talks and reflective about what makes a good talk. We hope the feedback was useful both to the presenters and to groups that presented later in the semester.

Select Student Response Sheets for Sample Presentation (PDF) (Courtesy of MIT students. Used with permission.)

The peer response sheets also served as an indication of attendance. Ten percent of the presentation grade was allocated to an attendance mark. Attendance was in fact quite high, and students often wrote to Haynes in advance if they had to be absent. In one case a student watched a flip-cam recording of a presentation he had to miss. We think the high attendance was largely a function of the high quality of the presentations, since all the teams gave very good presentations.

« Previous: Practice and Feedback

To illustrate the development and delivery of the student presentations, videos of a sample practice presentation and final presentation are below.

Sample Presentation: The Dynamics of Successive Differences Over ℤ and ℝ

This project developed from the project description for Number Squares (PDF) . To read the paper produced by this team of students and to view the debriefing video, see the Sample Student Papers page.

The presentations below are courtesy of Yida Gao, Matt Redmond, and Zach Steward. Used with permission.

Practice Presentation

This video features the student team’s practice presentation. After each individual presents his part, the group of students and instructors discuss improvements and changes.

Final Presentation

This video features the student team’s final presentation delivered in class.

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Rubric Best Practices, Examples, and Templates

A rubric is a scoring tool that identifies the different criteria relevant to an assignment, assessment, or learning outcome and states the possible levels of achievement in a specific, clear, and objective way. Use rubrics to assess project-based student work including essays, group projects, creative endeavors, and oral presentations.

Rubrics can help instructors communicate expectations to students and assess student work fairly, consistently and efficiently. Rubrics can provide students with informative feedback on their strengths and weaknesses so that they can reflect on their performance and work on areas that need improvement.

How to Get Started

Best practices, moodle how-to guides.

• Workshop Recording (Spring 2024)
• Workshop Registration

Step 1: Analyze the assignment

The first step in the rubric creation process is to analyze the assignment or assessment for which you are creating a rubric. To do this, consider the following questions:

• What is the purpose of the assignment and your feedback? What do you want students to demonstrate through the completion of this assignment (i.e. what are the learning objectives measured by it)? Is it a summative assessment, or will students use the feedback to create an improved product?
• Does the assignment break down into different or smaller tasks? Are these tasks equally important as the main assignment?
• What would an “excellent” assignment look like? An “acceptable” assignment? One that still needs major work?
• How detailed do you want the feedback you give students to be? Do you want/need to give them a grade?

Step 2: Decide what kind of rubric you will use

Types of rubrics: holistic, analytic/descriptive, single-point

Holistic Rubric. A holistic rubric includes all the criteria (such as clarity, organization, mechanics, etc.) to be considered together and included in a single evaluation. With a holistic rubric, the rater or grader assigns a single score based on an overall judgment of the student’s work, using descriptions of each performance level to assign the score.

Advantages of holistic rubrics:

• Can p lace an emphasis on what learners can demonstrate rather than what they cannot
• Save grader time by minimizing the number of evaluations to be made for each student
• Can be used consistently across raters, provided they have all been trained

Disadvantages of holistic rubrics:

• Provide less specific feedback than analytic/descriptive rubrics
• Can be difficult to choose a score when a student’s work is at varying levels across the criteria
• Any weighting of c riteria cannot be indicated in the rubric

Analytic/Descriptive Rubric . An analytic or descriptive rubric often takes the form of a table with the criteria listed in the left column and with levels of performance listed across the top row. Each cell contains a description of what the specified criterion looks like at a given level of performance. Each of the criteria is scored individually.

Advantages of analytic rubrics:

• Provide detailed feedback on areas of strength or weakness
• Each criterion can be weighted to reflect its relative importance

Disadvantages of analytic rubrics:

• More time-consuming to create and use than a holistic rubric
• May not be used consistently across raters unless the cells are well defined
• May result in giving less personalized feedback

Single-Point Rubric . A single-point rubric is breaks down the components of an assignment into different criteria, but instead of describing different levels of performance, only the “proficient” level is described. Feedback space is provided for instructors to give individualized comments to help students improve and/or show where they excelled beyond the proficiency descriptors.

Advantages of single-point rubrics:

• Easier to create than an analytic/descriptive rubric
• Perhaps more likely that students will read the descriptors
• Areas of concern and excellence are open-ended
• May removes a focus on the grade/points
• May increase student creativity in project-based assignments

Disadvantage of analytic rubrics: Requires more work for instructors writing feedback

Step 3 (Optional): Look for templates and examples.

You might Google, “Rubric for persuasive essay at the college level” and see if there are any publicly available examples to start from. Ask your colleagues if they have used a rubric for a similar assignment. Some examples are also available at the end of this article. These rubrics can be a great starting point for you, but consider steps 3, 4, and 5 below to ensure that the rubric matches your assignment description, learning objectives and expectations.

Step 4: Define the assignment criteria

Make a list of the knowledge and skills are you measuring with the assignment/assessment Refer to your stated learning objectives, the assignment instructions, past examples of student work, etc. for help.

  Helpful strategies for defining grading criteria:

• Collaborate with co-instructors, teaching assistants, and other colleagues
• Brainstorm and discuss with students
• Can they be observed and measured?
• Are they important and essential?
• Are they distinct from other criteria?
• Are they phrased in precise, unambiguous language?
• Revise the criteria as needed
• Consider whether some are more important than others, and how you will weight them.

Step 5: Design the rating scale

Most ratings scales include between 3 and 5 levels. Consider the following questions when designing your rating scale:

• Given what students are able to demonstrate in this assignment/assessment, what are the possible levels of achievement?
• How many levels would you like to include (more levels means more detailed descriptions)
• Will you use numbers and/or descriptive labels for each level of performance? (for example 5, 4, 3, 2, 1 and/or Exceeds expectations, Accomplished, Proficient, Developing, Beginning, etc.)
• Don’t use too many columns, and recognize that some criteria can have more columns that others . The rubric needs to be comprehensible and organized. Pick the right amount of columns so that the criteria flow logically and naturally across levels.

Step 6: Write descriptions for each level of the rating scale

Artificial Intelligence tools like Chat GPT have proven to be useful tools for creating a rubric. You will want to engineer your prompt that you provide the AI assistant to ensure you get what you want. For example, you might provide the assignment description, the criteria you feel are important, and the number of levels of performance you want in your prompt. Use the results as a starting point, and adjust the descriptions as needed.

Building a rubric from scratch

For a single-point rubric , describe what would be considered “proficient,” i.e. B-level work, and provide that description. You might also include suggestions for students outside of the actual rubric about how they might surpass proficient-level work.

For analytic and holistic rubrics , c reate statements of expected performance at each level of the rubric.

• Consider what descriptor is appropriate for each criteria, e.g., presence vs absence, complete vs incomplete, many vs none, major vs minor, consistent vs inconsistent, always vs never. If you have an indicator described in one level, it will need to be described in each level.
• You might start with the top/exemplary level. What does it look like when a student has achieved excellence for each/every criterion? Then, look at the “bottom” level. What does it look like when a student has not achieved the learning goals in any way? Then, complete the in-between levels.
• For an analytic rubric , do this for each particular criterion of the rubric so that every cell in the table is filled. These descriptions help students understand your expectations and their performance in regard to those expectations.

Well-written descriptions:

• Describe observable and measurable behavior
• Use parallel language across the scale
• Indicate the degree to which the standards are met

Step 7: Create your rubric

Create your rubric in a table or spreadsheet in Word, Google Docs, Sheets, etc., and then transfer it by typing it into Moodle. You can also use online tools to create the rubric, but you will still have to type the criteria, indicators, levels, etc., into Moodle. Rubric creators: Rubistar , iRubric

Step 8: Pilot-test your rubric

Prior to implementing your rubric on a live course, obtain feedback from:

• Teacher assistants

Try out your new rubric on a sample of student work. After you pilot-test your rubric, analyze the results to consider its effectiveness and revise accordingly.

• Limit the rubric to a single page for reading and grading ease
• Use parallel language . Use similar language and syntax/wording from column to column. Make sure that the rubric can be easily read from left to right or vice versa.
• Use student-friendly language . Make sure the language is learning-level appropriate. If you use academic language or concepts, you will need to teach those concepts.
• Share and discuss the rubric with your students . Students should understand that the rubric is there to help them learn, reflect, and self-assess. If students use a rubric, they will understand the expectations and their relevance to learning.
• Consider scalability and reusability of rubrics. Create rubric templates that you can alter as needed for multiple assignments.
• Maximize the descriptiveness of your language. Avoid words like “good” and “excellent.” For example, instead of saying, “uses excellent sources,” you might describe what makes a resource excellent so that students will know. You might also consider reducing the reliance on quantity, such as a number of allowable misspelled words. Focus instead, for example, on how distracting any spelling errors are.

Example of an analytic rubric for a final paper

Example of a holistic rubric for a final paper

Single-Point Rubric

More examples:

• Single Point Rubric Template ( variation )
• Analytic Rubric Template make a copy to edit
• A Rubric for Rubrics
• Bank of Online Discussion Rubrics in different formats
• Mathematical Presentations Descriptive Rubric
• Math Proof Assessment Rubric
• Kansas State Sample Rubrics
• Design Single Point Rubric

Technology Tools: Rubrics in Moodle

• Moodle Docs: Rubrics
• Moodle Docs: Grading Guide (use for single-point rubrics)

Tools with rubrics (other than Moodle)

• Google Assignments
• Turnitin Assignments: Rubric or Grading Form

Other resources

• DePaul University (n.d.). Rubrics .
• Gonzalez, J. (2014). Know your terms: Holistic, Analytic, and Single-Point Rubrics . Cult of Pedagogy.
• Goodrich, H. (1996). Understanding rubrics . Teaching for Authentic Student Performance, 54 (4), 14-17. Retrieved from   
• Miller, A. (2012). Tame the beast: tips for designing and using rubrics.
• Ragupathi, K., Lee, A. (2020). Beyond Fairness and Consistency in Grading: The Role of Rubrics in Higher Education. In: Sanger, C., Gleason, N. (eds) Diversity and Inclusion in Global Higher Education. Palgrave Macmillan, Singapore.

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Math Rubrics

Exemplars math material includes standards-based rubrics that define what work meets a standard and allows teachers (and students) to distinguish between different levels of performance.

Our math rubrics have four levels of performance: Novice , Apprentice , Practitioner (meets the standard), and Expert .

Exemplars uses two types of rubrics: 

• Standards-Based Assessment Rubrics  are used by teachers to assess student work in Math
• Student Rubrics  are used by learners in self- and peer-assessment.

Assessment Rubrics

Student rubrics, standards-based math rubric.

This rubric was updated in 2014 to reflect more current standards. It supports NCTM Process Standards and the Common Core State Standards for Mathematical Practice .

Classic 5-Criteria Math Rubric

This rubric was developed to reflect the revised NCTM standards.

Classic 3-Criteria Math Rubric

This rubric was used from 1993 to 2001 to assess student performance. It is based on the original NCTM standards. Many schools and districts using Exemplars earlier material continue to use this rubric to assess student performance.

Pre K–K Rubric

This rubric was developed to assess younger students' performance. It is based on recommendations from NCTM and the preschool standards developed at the Conference on Standards for Prekindergarten and Kindergarten Mathematics Education.

Jigsaw Rubric

This rubric uses pieces of a jigsaw puzzle as symbols. It is appropriate to use with younger students who may not be able to follow the words in another rubric.

Thermometer Rubric

This rubric is appropriate to use with older children. They can self-assess by drawing a line on the thermometer. The teacher can also assess by making a mark on the same rubric.

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• Resource Library
• 7th Grade Mathematics
• Problem-Solving

Education Standards

Maryland college and career ready math standards.

Learning Domain: Statistics and Probability

Standard: Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation.

Standard: Understand that, just as with simple events, the probability of a compound event is the fraction of outcomes in the sample space for which the compound event occurs.

Standard: Represent sample spaces for compound events using methods such as organized lists, tables and tree diagrams. For an event described in everyday language (e.g., "rolling double sixes"ť), identify the outcomes in the sample space which compose the event.

Standard: Design and use a simulation to generate frequencies for compound events. For example, use random digits as a simulation tool to approximate the answer to the question: If 40% of donors have type A blood, what is the probability that it will take at least 4 donors to find one with type A blood?

Common Core State Standards Math

Cluster: Investigate chance processes and develop, use, and evaluate probability models

Standard: Represent sample spaces for compound events using methods such as organized lists, tables and tree diagrams. For an event described in everyday language (e.g., “rolling double sixes”), identify the outcomes in the sample space which compose the event.

Project Rubric: Making Connections

Project rubric: putting math to work, project rubric & criteria.

Students design and work on their projects in class. They review the project rubric and, as a class, add criteria relevant to their specific projects.

Key Concepts

Students are expected to use the mathematical skills they have acquired in previous lessons or in previous math courses. The lessons in this unit focus on developing and refining problem-solving skills.

Students will:

• Try a variety of strategies to approaching different types of problems.
• Devise a problem-solving plan and implement their plan systematically.
• Become aware that problems can be solved in more than one way.
• See the value of approaching problems in a systematic manner.
• Communicate their approaches with precision and articulate why their strategies and solutions are reasonable.
• Make connections between previous learning and real-world problems.
• Create efficacy and confidence in solving challenging problems in a real-world setting.

Goals and Learning Objectives

• Create and implement a problem-solving plan.
• Organize and interpret data presented in a problem situation.
• Use multiple representations—including tables, graphs, and equations—to organize and communicate data.
• Articulate strategies, thought processes, and approaches to solving a problem and defend why the solution is reasonable.

Project Rubric

Lesson guide.

Have students view the project rubric. Give students a minute to study the rubric. Then have students take turns saying one thing about the rubric without looking at it.

When students are finished, tell them that today they will add any specifics to the rubric that they think are needed for evaluating their projects.

SWD: Students with disabilities may have a more challenging time identifying areas of improvement to target in their projects. Teach your students how to review a project using the rubric and a sample project. Model for students how to evaluate their project to ensure they are completing all components needed and identifying any areas that need to be addressed that are not in the rubric.

Work with a partner to review the project rubric.

• Take a few minutes to study the rubric by yourself.
• Without looking at the rubric, take 1 minute to describe the rubric as completely as possible to your partner (who can look at the rubric). Your partner should listen carefully to your description.
• Briefly look at the rubric again. Your partner should now take 30 seconds to add to your description of the rubric—without repeating any of your description and without looking at the rubric.

Math Mission

Discuss the Math Mission. Students will work on their projects and evaluate their progress using the project rubric.

Work on your project, and evaluate your progress using the project rubric.

Organize and Analyze Project Data

Make sure students understand that the best use of this in-class project work day is to accomplish what they can't easily do later outside of class. Big, beautiful displays are a last step; now is the time for groups to decide how they will go about completing their project. Today's work is messy and preliminary; some of it may be devoted to finding resources (Internet-based and elsewhere).

Circulate among the working pairs and groups—listening to what they say and watching what they do. Ask clarifying questions:

• What mathematical concepts can you use to investigate your question?
• What materials are necessary?
• How will you investigate your question?
• How can you use units to clarify your results?
• How will you communicate your results to your audience?

SWD: Some students with disabilities may struggle with time management, create a timeline and “to do list” for students so they know where their progress should be regarding project completion. Hang this information in a prominent location in your classroom.

Today you will:

• Conduct research to gather information or collect data.
• Organize your information or data.
• Analyze your information or data in order to answer your question.

As you work on your project, consider these questions:

• What mathematical concepts do you need to use in order to investigate your question?

Examples: Numerical reasoning, probability, statistics, geometry, ratios and proportional relationships, expressions, and equations

• How will you communicate your conclusions to the class?

Examples: Diagrams and graphs, equations, verbal explanations, and models

As you work, use the project rubric to evaluate your progress and make sure you are on the right track.

Your Completed Project

Go over the list of what the presentations should include.

Your completed project should include:

• The information or data you researched.
• Graphs or diagrams that communicate your findings.
• Expressions, equations, or formulas that you used to make your conclusions.
• A summary of your findings.
• Your conclusions regarding your specific question.

Make Connections

Have students return to the project rubric. Tell them that, as a class, they can agree to add to—but not subtract from—the general rubric to improve the fit with their problem-solving projects.

There are two main ways to add to the rubric:

• Add detail to one or more of the descriptions of score 4.
• See the column “Specific to This Project.”
• Add a new criterion for scoring, and then describe the score 4 for that criterion. See the blank, last row.

Give students a couple of minutes to talk with their partner or group. Then let individuals propose any specific additions. You or a student may record these additions, and after the class discussion, adopt whichever criteria have the support of the class.

Note that this is a brief, focused opportunity for students to take ownership of the rubric. They may make several additions or none. The objective is their buy-in.

Performance Task

Ways of thinking: make connections.

Look at the rubric again.

• Notice the blank column with the heading “Specific to This Project.” Is there anything that you think should be added to this column?
• Next, look at the bottom row that is blank. Is there any scoring criterion for the project that you think should be added here?

Take a few minutes to discuss these questions with a partner.

• Write down any ideas you have.
• Discuss your ideas as a class. As you propose an idea make sure to explain why you think it is important. After all ideas are discussed the class will decide as a group whether to adopt any of the suggestions.

Reflect on Your Work

Give students a few minutes to respond individually to two simple prompts, focused on what they accomplished today and what their next steps are. These reflections can be quite skeletal—very short lists are fine.

Then give partners and groups a few more minutes to share their individual reflections.

Make sure students realize that their reflections now serve as their starter for the work they will do outside of class to complete their problem-solving project.

ELL: The “Reflect on Your Work” section provides opportunities for ELLs to develop literacy in English and proficiency in mathematics. Make sure students use both academic and specialized mathematical language when reflecting on their project. Give students time to discuss the summary before they write, and make sure students create a task list for completing their project based upon the rubric.

Write a reflection about the ideas discussed in class today. Use the sentence starters below if you find them to be helpful. After you have finished, share your reflections with your group.

Today my group accomplished…

Our next steps are…

Version History

Providing clarity, inspiration and resources for Mathematics in the MYP

How to write MYP Maths Criterion C Assessments - Tips and Examples

Updated: Jul 31, 2022

Communication is a common feature in the IB; it appears as an ATL skill, a learner profile trait and again as an assessment objective. Let’s break down how we assess communication in MYP Mathematics.

The criterion strands

i. use appropriate mathematical language (notation, symbols and terminology) in both oral and written explanations

- Give an opportunity for students to use the keywords introduced in the unit.

- It should be clear that students should always use, and recognise, the mathematical notation given in the maths guide (pages 47 - 50)

- Opportunities to present, teach or create a video will allow oral explanations

ii. use appropriate forms of mathematical representation to present information

iii. move between different forms of mathematical representation (not in year 1)

-Forms of mathematical representation include: written explanations, calculations, diagrams, tables, graphs, lists, formula/ratio triangle, conversion loops, flowcharts, number lines, formulae, proof and essentially anything that SHOWS their thinking.

-The most “appropriate forms” of representation should have been modelled throughout the unit - if they would be expected to draw a graph in the assessment, time should be spent on how to scale axes. With trigonometry they should have seen how to label the sides of a triangle. If looking at algorithms they should know they correct symbols for a flowchart and have had practice drawing them. For proof, they should understand how to lay that out.

- "Moving between" appropriate forms could involve creating them, or interpreting them. So make sure pupils have experience with both.

- Interpretation of simulations, images, videos, animations, data tables and graphs will be required for the e-assessment.

iv. communicate coherent (year 1+), complete (year 2+) and concise (year 4+) mathematical lines of reasoning

-Coherent - does it flow? Is it clear to the audience where answers came from or how a diagram links to a conclusion?

- Complete - share all thinking, calculations and steps. Sometimes it helps to give the project a mock audience of someone a few years younger than the class, so they remember to explain what they are doing.

- Concise - refine and share what is necessary. Particularly in reports, it is important points aren’t repeated while still ensuring communication is complete and flows.

v. organize information using a logical structure.

-Beginning, middle, end - title, introduction to explain the investigation or problem, main body showing the processes they took, conclusion with final rule (criterion B), answer or reflection (criterion D).

- In a report, subheadings can help to guide the reader

- In a presentation, each slide should have its own purpose

- In a poster, it should be clear what direction to read the information

- A video should still have a beginning, middle, end

What it says in the guide

“Criterion C is often used to assess constructed responses and reports in combination with criterion B or D.” (page 31)

“Investigations and real-life problems

Reports that:

• require logical structure

• allow multiple forms of representation to present information.

Criterion C is often used when students present a report, for example, that requires a logical structure in order to be followed and that would allow for several forms of representation to be used to present information.” (page 31)

In reference to the e-assessment: “For example, a question assessing knowledge and understanding may also require students to move between different

forms of mathematical representation.” (page 47)

Some examples

A poster to show the impact of vaccinations on measles outbreaks around the world. Include data tables from different countries, algebraic and graphical communication of exponential functions. (criteria C, D)

An investigation on how to set the rules to make certain dice games “fair” may involve sample space diagrams showing how different rules result in different outcomes. A slideshow presentation would clearly distinguish between the different investigations on each slide. (criteria B, C)

An instructional video about writing numbers as composition of prime factors would assess the use of mathematical language verbally. (criteria A, C)

Through a video, animation or set of images, students can see an investigation or mathemagic trick being completed step by step. Their task is to create a flow chart which outlines the steps that have been taken. Nrich has some great ones!

Good practice and tips

-Not every strand has to be assessed - either structure the assessment to ensure students can meet every strand or critique your assessment and remove the ones that do not seem applicable.

-In the younger years, give students a checklist of what to include to aid reflection before submitting. This can be in addition to the task-specific clarification. It can include “my introduction mentions which sport I am investigating” or “my work falls under the subheadings: patterns, rule, verification, justification” or “my conclusion talks about how accurate my answer is”.

-Criterion C is assessed alongside A, B and D in the e-assessment so it is beneficial for students to see it in different contexts beforehand. Criteria A can easily be as a response to a visual aid or require mathematical language/notation and involve showing working. It will be harder to assess some of the strands in a test format so save strand v), for example, for another assessment.

-If criterion C is assessed with another criterion, make sure it is clear to the students (and you) how each question will be graded. Give students an opportunity to be successful on C even if they can not find a rule or solve the real-life problem.

- Prior to the summative, encourage peer assessment (in a safe and positive environment). If a student is struggling to follow what another student created, give them a constructive outlet to give feedback.

Here are two examples of criterion C being assessed within an investigation and real-life problem. They include the task, assessment rubric, task-specific clarifications, sample student answer and marking guidelines.

Recent Posts

How to write MYP Maths Criterion A Summative Assessments

How to write MYP Maths Criterion B Assessments - Tips and Examples

How to write MYP Maths Criterion D Assessments - Tips and Examples

Feedback and assessment for presentations

Range of instructor feedback, specificity of instructor feedback, advantages of various forms of feedback, rubrics and grading/commenting forms.

Encourage students to improve their presentations: otherwise presenting repeatedly may merely ingrain bad habits. Feedback can come from peers and from instructors.

Consider commenting on the following:

• Timing notes: an outline of the talk including the amount of time spent on each portion.
• Feedback on the presentation style: style of speech, use of visual aids (blackboard/ slides/ images), pacing, audience engagement.
• Feedback on mathematical content: correctness, connections of material to other parts of course or other parts of mathematics (this is a good way to pique students’ interest in the subject matter).
• Feedback on teaching strategy: providing motivation, examples, conceptual explanations, repetition, etc.
• See also the general principles of communicating math .

Issues specific to various forms of presentations can be found on the page Assignments on Presentations .

The level of detail of the comments depends on whether the presentation will be given again. For example, noting every math mistake might be appropriate for a rehearsal so the student can be sure to fix those mistakes, but if the presentation will not be given again, a list of every mistake could be demoralizing with little positive benefit. At this point, comments should be more general and should focus instead on the sorts of things to consider for future presentations.

For other issues to consider when choosing and wording comments, see the handout Dimensions of Commenting .

• Most efficient is to take notes during the presentation and give them to the student immediately after the presentation.
• Most helpful for the student (but time intensive) may be to record the presentation and then sit with the student to review the recording.
• Another option is to discuss the presentation as a class immediately after the presentation. For this option to be successful, a respectful, collegial atmosphere is necessary.
• If you prefer time to think before giving feedback, you could e-mail your response after class or arrange to meet with the student at a later date. Meeting may be more efficient than e-mail because the student can ask clarifying questions so you don’t have to take the time to make your notes self-explanatory.

Identifying and prioritizing grading criteria before grading is important to prevent unintentional, subconscious bias,  even in graders who consider themselves objective,  as found by this study of hiring decisions based on criteria prioritized before/after learning about an applicant: Uhlmann and Cohen, “ Constructed Criteria: Redefining Merit to Justify Discrimination ,” Psychological Science, Vol 16, No 6, pp. 474-480, 2005.

Guidance for how to create a rubric is provided on the MAA Mathematical Communication page “ How can I objectively grade something as subjective as communication ?”

For classes in which each student gives multiple presentations, see the grading suggestions on the page for undergraduate seminars .

Sample grading criteria & rubrics for presentations are provided below.

Using a commenting form or grading form can remind you to consider all aspects of presentations that you’ve decided are important, rather than focusing only on the most obvious issues with any given presentation. A commenting form or grading form can also help you to find positive aspects of a presentation that on first consideration seems to be thoroughly troublesome. Some examples of forms and rubrics are below, but it’s best to make your own so the form reflects your priorities.

• Pedro Reis’ presentation evaluation form for M.I.T.’s Undergraduate Seminar in Physical Applied Mathematics , a topics seminar
• Characteristics of an effective undergraduate research talk : outlines basic expectations, characteristics of a good talk, and characteristics of an excellent talk
• Jardine, D. and Ferlini, V. “Assessing Student Oral Presentation of Mathematics,”   Supporting Assessment in Undergraduate Mathematics , The Mathematical Association of America, 2006, pp. 157-162 . This report of a department’s assessment of the teaching of math presentations contains a rubric for individual presentations. See Appendix B.
• Dennis, K. “Assessing Written and Oral Communication of Senior Projects,”  Supporting Assessment in Undergraduate Mathematics , The Mathematical Association of America, 2006, pp. 177-181 . Contains rubrics for presenting and writing, with recommendations.
• Rubric for Mathematical Presentations from Ball State University
• A description of criteria for math oral presentation for a math majors’ seminar, with categories Logic & Organization, Content, and Delivery.
• Form for commenting on and grading a presentation of a proof
• Scoring Rubric for Math Fair Projects with an audience of children
• Rubric for grades 6-8 for a math talk about solving two-step equations with one variable

What is Math Comm

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