Unit 3: Assessment & Feedback


Now that we know what problem-based learning is, what it looks like in a math classroom, and how to design problematic tasks it is now time to learn about the methods of assessment and feedback.

Unit Objectives:

At the end of this unit you will be able to do the following:

  • When given examples you will identify and describe different methods of appropriate assessment and feedback in writing.



Before reviewing and discussing specific methods of assessment; read the following short article. While reading jot down a few notes regarding the following prompts; What are some alternative assessment methods? How might they help students in any classroom? More specifically in a math classroom? Assessing the Effectiveness of Problem‑Based Learning in Higher Education: Lessons from the Literature. (Note: After reading the article you will have to use the back button on your browser to return to this page.)

Assessments & Evaluation:

Our ability to successfully assess students, using both formative and summative evaluations, in a problem-based environment has direct implications on the effectiveness of instruction. According to Darling-Hammond there exists three elements of assessment that are important for meaningful learning.

  1. Designing performance assessment: Teachers must design authentic tasks that apply concepts to real life situations and other disciplines. (Problematic tasks that we learned about in the previous unit).
  2. Creating evaluation tools: Teachers must create rubrics and observation checklists with the students so that they can see what constitutes ‘good’ work. These evaluation tools therefore act as the guidelines to the authentic tasks described above.
  3. Formative assessment: Teachers must continually provide feedback on assignments the students are working on.

“Research suggests that thoughtfully structured performance assessments can support improvement in the quality of teaching, and that inquiry-based learning demands such assessments both to define the task and to properly evaluate what has been learned” (Darling-Hammond, 2008, p. 64). Thus, after the authentic and problematic tasks have been created and implemented the teacher must be able to accurately evaluate the students progress. However, how does he or she do this? To begin, teachers can create rubrics and observation checklists so that they, and their students, understand what is being asked for, in the final product. But, evaluation tools only begin here. Problem-based inquiry requires alternative assessment strategies to ensure the students are engaged in meaningful learning. Look at the list of strategies below to see some evaluation practices implemented today; note some of these are those you have read about in the above article.

  • Expert evaluations: Problem-based learning replicates those situations encountered in the real world, perhaps in the workplace or in everyday life. So what better way to evaluate a student’s knowledge base and content understanding than from an outside source such as an expert. The students will not only be gaining knowledge in mathematics but they will also gain ‘career knowledge,' accepting and putting to use the positive and negative criticism given by the experts. The students and teacher will be able to use this evaluation to improve current and/or future projects.

  • Peer Evaluations: Students must be able to work cooperatively and successfully on a team. The evaluation from peers will not only help the teacher see where the students are in terms of the content, the process, and the end product, but it will also help the students learn about shared responsibility, the importance of deadlines, the need to be disciplined, and the importance of communication. Problem-based environments and those in the real world value the importance of teams, so this type of assessment should be used as often as possible in the classroom.


  • Self-Assessment: This type of assessment is one in which students judge their own projects, papers, and presentations. This therefore gives students the opportunity to monitor their own progress. Thus, students think more carefully about what they do know and do not know in relation to the given task. As a result, this type of assessment is critical for the development of [metacognitive skills] and should be used as often as possible in an environment that uses and supports problem-based learning.


  • Reflective Journals: This assessment method reveals what the students have been learning. Now these journals can be utilized weekly, monthly, or throughout each unit but the outcome of such reflection is important. According to MacDonald, “students tend to be more open and honest about their learning than one would expect and these can be criterion referenced” (MacDonald, 2005, p. 90). As a result, misconceptions, misunderstandings, and certain revelations could be revealed or discovered through such journaling.


  • Portfolios: This is a collection of work in which students place revised projects and other pieces of work that they have been working on throughout the course of the semester or year. This can then be looked at by the teacher to see the progress made by each student. This type of assessment allows teachers to comment on different aspects of student's work (assessing their content knowledge and their problem-solving abilities) while giving students the feedback needed to continually improve their thinking. To look at an example of a Pre-Algebra portfolio of a math project that revolved around problem-based learning, please visit the following website Pre-Algebra Sample Portfolio. (Note: In order to return to this page, you will need to use the back button on your browser.)

  • Exams: There is nothing wrong with exams; however they should replicate the ideas of problem based learning. MacDonald explained this so well that I did not want to change or add anything to the explanation
  • “The students should engage in pre-examination activities which reflect the type of learning activities they have experienced previously, including working in groups. Treat the examination as a time-constrained activity (anything from 30 minutes to a week) where the students may have to work individually with new data or scenarios and have to make sense of the new situation. The students should not have to do ‘revision’ in the traditional sense of learning by rote, though they will have to prepare for the examination. A second challenge would be to have students spending a substantial proportion of the time thinking, working with ideas and not simply writing down the facts they have remembered” (MacDonald, 2005, p. 90).

  • Reports: These reports serve two purposes in a mathematics classroom. First as a way for students to develop their own mathematical thinking and second as a guide for teachers to assess and plan instruction. These reports allow the teacher to see where the students are and give the students a chance to explain and expand their ideas. Learning mathematics without explicit writing limits the opportunities for students because there are limits to the communication between the student and teacher. In a problem-based learning environment such assessment gives students the opportunity to explain, clarify, and defend solution methods. (Kenney et al., 2005, p. 50).


Rubrics: The students and the teacher should evaluate the below assessment methods using a rubric that was designed and agreed upon by both parties.

  • Individual Presentations: Students are asked to present their work or solution method to the class or other members of the community to reveal their contribution to the given problem scenario.
  • Group Presentations: Students, may or may not, have individual roles to take on, but the task should be authentic in nature and be evaluated based on the work handed in by individual members of the group and by the group as a whole.
  • -To look at some examples of rubrics that correlate with the theme of problematic mathematics, take a look at the following website; Rubrics: Math Problem-Solving. (Note to return to this page, after reading through the rubric, you will need to use the back button on your browser).


  • All of the strategies above have one very important similarity, they are all examples of formative assessment and as a result provide continuous feedback to students. This formative feedback, through self, peer, and teacher-assessment, help students learn to reflect on their own work, evaluate it against a rubric, and continuously improve their ways of thinking. Students need to spend time learning for understanding and transfer and less time memorizing facts and procedures from textbooks or lectures. Since, according to the book How People Learn, "in order for learners to gain insight into their learning and their understanding, frequent feedback is critical: students need to monitor their learning and actively evaluate their strategies and their current levels of understandings."

  • So how can teachers provide effective feedback to their students? Well besides implementing and using the above strategies we can turn to the following article and learn a bit more about this question: Focusing on Feedback. While reading, think about the different ways that these ideas could be used a math classroom that implements problem-based inquiry. (Note: To return to this page you will have to use the back button on your browser).

Pencil.jpg Reflection:

After analyzing the above strategies and working through the unit, take a few minutes and reflect on your understanding. Think about the following prompts:

  1. What is the difference between summative and formative assessment? How does this relate to the ability to give feedback?
  2. What are three different ways to assess students participating in PBL? Why are they effective methods?

Final Thoughts:


Thank you so much for participating in this mini course; I hope you have found the course informative and interesting. Moreover, I hope you walk away today with a better understanding of problem-based inquiry in relation to the mathematics classroom. My hope is that you will take the information gained from this course and utilize it in your classroom.

References and Resources:

201 math problem solving. (n.d.). Retrieved from http://web.njit.edu/~ronkowit/teaching/rubrics/samples/math_probsolv_chicago.pdf

Darling-Hammond, ML. (2008). Powerful learning:what we know about teaching for understanding. San Francisco, CA: Jossey-Bass.

Focus of effectiveness: researched-based strategies. (2005). Northwest Regional Educational Laboratory, Retrieved from http://www.netc.org/focus/strategies/prov.php

Kenney, J, M., Hancewicz, E, Heuer, L, Metsisto, D, & Tuttle, C, L. (2005). Literacy strategies for improving mathematics instruction. Alexandria, VA: Association for Supervision and Curriculum Development.

Macdonald, R. (2005). Assessment strategies for enquiry and problem-based learning. Handbook of Enquiry & Problem Based Learning. Retrieved from http://www.nuigalway.ie/celt/pblbook/chapter9.pdf

Major, H, C., & Palmer, B. (2005). Assessing the effectiveness of problem‑based learning in higher education: lessons from the literature. Academic Exchange Quarterly, 5(1), Retrieved from http://www.rapidintellect.com/AEQweb/mop4spr01.htm

Math 815: pre-algebra portfolio sample. (n.d.). Retrieved from http://webenhanced.lbcc.edu/mathbm/math815bkm/coursedocs/815.pdf


Kaitlyn's Portfolio Page

Return to Problematic Mathematics: PBL designed for the math classroom

Unit 1: What is problem-based learning & why is it beneficial?

Unit 2: Designing Problematic Tasks

Unit 3: Assessment & Feedback

Extended Resources (PBL in math)