Project-Based Learning & Assessment
In Mr. Ho's MDM4U1 (Grade 12, Mathematics of Data Management) class, his students are provided with an opportunity for inclusive, interdisciplinary, and equitable learning near the end of the course. They work in groups or individually on a course culminating project, which consists of Part 1: Probability - Game of Chance and Part 2: Statistics - Survey. In Part 1: Probability - Game of Chance, the students design and create their own probability games using dice, spinners, coins, papers, cards, and computer programs/simulations (e.g., micro:bit technology). In Part 2: Statistics - Survey, the students create their own research questions related to math and other courses and then design a bias-free survey to help them answer their research questions. Then, they give this survey to their selected group of target audience to complete, analyze/present the results using statistics, and then make their conclusion.
Learning Outcomes: Part 1: Probability - Game of Chance
Here are pictures of some selected samples of student work on games of chance:
Learning Outcomes: Part 2: Statistics - Survey
Here are screenshots of some selected samples of student work on survey design and analysis:
What is the main challenge for the MDM4U1 teacher running this project-based assessment?
The main challenge for the MDM4U1 teacher running this project-based assessment is "how to mark the student's work." In almost all the units in any math courses, not just MDM4U1 (Grade 12, Mathematics of Data Management), a summative assessment is often a test with typical math textbook-based questions. Students would get 1 mark for each correct key step they show in each question of the test, and they would lose 0.5 marks or 1 mark for each mistake they make in a question. However, this project consists of components more than just typical math textbook-based questions. It is impossible for the MDM4U1 teacher to only follow this traditional math marking scheme.
An alternative approach is to design and create a rubric for each requirement, with levels ranging from level 1 (limited understanding) to level 4 (thorough understanding). A possible problem is then how the MDM4U1 teacher efficiently, consistently and accurately determines if a piece of the student work shows limited, some, considerable, or thorough understanding across all MDM4U1 classes. For example, if a student asks their MDM4U1 teacher why their work is level 3, but their classmate's work is level 3+, how will the MDM4U1 teacher justify his/her decision in a convincing manner? What are the criteria for getting level 3 and level 3+, for example? If a student makes one mistake, does this mean they will get one sublevel down in the rubric system? If not, then how many mistakes does a student need to make before they will get one sublevel down in the rubric system? What is a fair way to interpret "limited," "some," "considerable," and "thorough" understanding of the student work when assessing this math project? By the way, students need to know all this before they start working on this math project. How would the MDM4U1 teacher address all these issues?
What is the solution proposed by Mr. Ho and his PLC colleagues?
Mr. Ho consulted with a TDSB hybrid-teacher coach in an online meeting at lunch for ideas in September 2024 and then worked with his colleagues (e.g., Sarah Peeren, Esther Tello, Raymond Chung, Ken Smith, Luciano Pattara, and Peter Bartha) in the PLC group of "Driving Assessment through Inclusive Practice" in the 2024-25 school year at LP to come up with a solution.
Mr. Ho and his PLC colleagues came up with a marking scheme that involves the use of checklists. They constructed a page of checklists, which outline the requirements that do not involve calculations. Each checklist has a checkbox, each worth one mark; however, partial marks for each checkbox are possible in some circumstances. The MDM4U1 teacher just checks off each requirement of the project that does not involve calculations when they see that their student's work meets the requirement. When marking the student's work that involves calculations, the MDM4U1 teacher would use the traditional math marking scheme and then report the results in a continuum scale from 0 (no/limited knowledge) to 5 (through knowledge). Then, the MDM4U1 teacher tallies the checkmarks in all checkboxes and adds this to the marks of the continuum scales of requirements that involve calculations. The resulting total is the overall mark for this course culminating project. This is Mr. Ho's and his PLC colleagues' proposed solution, which would then help the MDM4U1 teacher efficiently, consistently, and accurately grade this course culminating project.
Sample of Mr. Ho's MDM4U1 Project-Based Asssessment
What do Mr. Ho's students think about this project-based learning and assessment?
Mr. Ho plans to give a survey to each of his MDM4U1 students at the end of the upcoming 2025-26 school year to gather their feedback on this project-based learning and assessment. He also plans to use the results of this survey for future improvements in course and assessment planning, design, and implementation, and to publish his findings here by the end of the 2025-26 school year.
Mr. Ho's and His Students' Wonderful Memories
Here are the videos capturing Mr. Ho's and his MDM4U1 students' wonderful memories with this project-based learning: