Assessāre is a Late Latin frequentative verb derived from assess, the inflectional stem of the past participle assessus, from the Latin verb assidēre “to sit next to or by ”.1
Assessment and evaluation require thoughtful planning and implementation to support the learning process and to inform teaching. All assessments and evaluation of student achievement must be based on the outcomes in the provincial curriculum and allow for flexibility determined by the needs of the student. “Mathematics is as much an aspect of culture as it is a collection of algorithms,”2 Assessment practices must be culturally valid as well as algorithmically valid.
When we place an excessive value on test scores or grades, we communicate fixed mindset messages to our students. families and teachers see children as the words that label them; “high,” “average” or “low.” Students quickly take ownership over their status. For example, students may take on the label of a “C” student and resign themselves to an incorrect belief that this reflects some innate mathematical capability and that working harder will not change that. (Boaler, 2020).
There are three interrelated purposes of assessment. Each type of assessment, systematically implemented, contributes to an overall picture of an individual student’s achievement.
How much assessment evidence is enough?
Since Saskatchewan math curricula contain learning outcomes by grade, the simple answer is: When the student has demonstrated clear understanding of the outcome. When considering assessment, it is important to focus on outcome attainment over product. What evidence do you have that a student has met the outcome? There is no timeline for when a student must demonstrate an understanding. Students have an entire school year to demonstrate achievement of outcomes.
In an effort to earn a decent grade in an abstract mathematics course, Simeonov (2016, pp. 442-443) pointed out that most students memorize without meaningful understanding. Students learn to hate mathematics, and then as families, they infuse their attitude into their children for elementary teachers to confront.3
A note about “spaced practice”:
Teachers may assign more tasks that are not necessarily evaluated but are intended to consolidate learning. This ensures that concepts are not taught in isolation, memorized and then forgotten. Evidence-based practice would assume that the student is able to demonstrate their understanding at any point in time. Spaced practice enables consolidation of learning. Key outcomes are revisited throughout the year. Spaced practice may also provide multiple opportunities for students to demonstrate understanding over time.
Quality, balanced assessment is the goal, keeping in mind the importance of holistic assessment (gathering data from multiple perspectives), triangulation of data, and the importance of cultural relevance.
…having a myriad of marks in the marks book is not necessarily a desirable objective.4
Education Sector Strategic Plan (ESSP) Math Data Collection
When gathering data to inform the placement of students on the holistic math rubric, the intent is to look at multiple samples of work done throughout the year specifically within the number strand. Any of the assessment tools and strategies suggested in this section can, and should, be used to inform one’s professional judgment to make a holistic determination of students’ understanding.
1Definition of assess | Dictionary.com. (n.d.). Retrieved 6 July 2020, from https://www.dictionary.com/browse/assess.
2Boyer, C., 1959. The rainbow from myth to mathematics. New York: T. Yoseloff.
3Meyer, S., et al. (2019) Culture-Based School Mathematics for Reconciliation and Professional Development. McDowell Foundation. p. 49. Retrieved 5 July 2020 from https://mcdowellfoundation.ca/?s=Culture+based (download the document here: https://saskmath.ca/wp-content/uploads/2021/09/culture-based_math.pdf
4Alberta Assessment Consortium. (n.d.) Collecting Evidence of Learning. Retrieved 9 July, 2020. https://aac.ab.ca/hot-topics/communicating-and-reporting/collecting-evidence-of-learning/