Do you ever wonder if mastery of standards is the same thing as proficiency in state standards? This is the question I have been thinking about today. Defining similar words that have distinct connotations is important. I often collaborate with teachers in different states to help define what “proficient” or “college-and-career ready” standards-based thinking looks like (I will use the term proficiency here). In this context, proficiency has a strong summative meaning about the expectation for what students cumulatively should know and be able to do by the end of the year. During these conversations, I often hear teachers and instructional leaders discuss mastery of each standard. While the two are related, they may not be interchangeable. Here is why.
Guskey (2010) writes that mastery learning (sometimes called standards-based or competency-based grading these days) is centered in the belief that students earn a grade based on achieving mastery. He writes students who need multiple opportunities to master the learning target deserve the same grade as those who mastered the learning target faster (yes!). To be related to proficiency, mastering a standard should mean that a student is successful in answering the less complex to more complex parts of the standard correctly.
Many standards have multiple parts. Thinking about how those separate pieces increase in sophistication is important. If the mastery expectation is set too low, a mastery approach in the classroom may not help move students to proficiency.
This Common Core standard is a great example: http://www.corestandards.org/Math/Content/3/MD/D/8/
“Solve real world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters.”
Questions to ask:
How might the learning targets inside this standard be sequenced to discover what mastery of the standard represents?
Are solving real world problems more or less difficult than mathematical ones? Should we use mathematical problems as a mastery demonstration of the standard or is this a precursor learning target to real world problem solving?
Is finding the perimeter given the side lengths the mastery point? Is it finding an unknown side length? How about exhibiting rectangles with the same perimeter and different areas in a word problem?
How does this standard fuse in and support the idea of mastery?
“Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.”
Should students be exhibiting rectangles with the same perimeter and different areas using easier math facts or more difficult math facts?
How might this mathematical practice be fused in and support the idea of mastery?
“Construct viable arguments and critique the reasoning of others.”
Should students be proving two different rectangles with same area can have different perimeters?
If you are tracking standard by standard, you might have conversations with other teachers about the level of rigor you expect regarding what students can do for mastery, and you might consider investigating what students are answering correctly: is it the less complex or more complex parts of the standard, with or without an associated mathematical practice?
Wiggins (2013/2014) is critical of dividing the parts of the whole for fear we will not present students with cognitively challenging opportunities to transfer what was learned to novel contexts. We might “dumb down” what mastery should represent. He defined mastery this way:
“Mastery is effective transfer of learning in authentic and worthy performance. Students have mastered a subject when they are fluent, even creative, in using their knowledge, skills, and understanding in key performance challenges and contexts at the heart of that subject, as measured against valid and high standards. “
Wiggins (2013/14) defined mastery in much the same way teachers define proficiency on state assessments. He is also alluding to the need for performance tasks, from my perspective. The key concept here is that “that you can draw on a repertoire of skills and knowledge effectively.”
Enter Rohrer, Dedrick, & Stershic, (2015) who have been investigating how to support students in retaining previously learned skills as well as show transfer of them. If you are a mathematics teacher, you may find this article useful!
Following the ideas of Rohrer, Dedrick, and Stershic, mastery of a standard may mean a student can choose a correct strategy for a problem and respond correctly when it is not obvious which strategy is needed. This may preclude a unit test from being the point at which mastery is measured.
Proficiency means children are independent thinkers, problem solvers, and managers of complexity in the content or course we are teaching by the end of the year. Because they are thinkers and problem solvers, they are INDEPENDENTLY transferring their learning to new situations we have not necessarily explicitly taught. While students may have mastered content for a specific unit, when they are tested on a unit (e.g., multiplication) they do not have to problem solve which procedure to use. It is for this reason that is critical to model thinking and problem solving for students where they have to make decisions on how to enter a problem (which operation should I use?).
As part of high-quality instruction, we have to give students opportunities to generalize and use skills outside of the unit of instruction to see if they retain what they have learned across time and use those skills as precursor skills for more difficult standards. Studying different models of cognition (higher order thinking skills) is critical to recognizing where students are in their learning as well as fostering their growth and development. Mastering a standard at a particular depth of complexity is different from integrating across standards to think through authentic problems. This is why it is so important to purposefully find places in your curriculum where you are layering in more complex tasks that require students to extend their thinking. I argue performance tasks are often the best tools for these purposeful increases in complexity that grow across the year.
In conclusion, mastery of content and skills in isolation may be an important precursor to proficiency, but it is likely different than being proficient in the state standards. The more standards that are mastered makes it more likely a child will be proficient, but this depends on when you are measuring mastery and how you are conceptualizing it. Standards really do not function in isolation, they are parts of a whole. Being proficient means students are handing easier and more difficult content from multiple standards and using higher order thinking skills at the same time. It does not mean students are perfect. But it does mean there is strong evidence that they are synthesizing information and authentically thinking in the discipline being measured.
I hope that you engage in these conversations with your fellow teachers, because they are critical for helping us make our classroom assessments actionable!
Guskey. T. (2010). Lessons of Mastery Learning. Educational Leadership, 68(2), 52-57 Retrieved from http://www.ascd.org/publications/educational-leadership/oct10/vol68/num02/Lessons-of-Mastery-Learning.aspx
Rohrer, Dedrick, & Stershic, (2015). Interleaved practice improves mathematics learning. Journal of Educational Psychology, 107(3), 900–908.
Wiggins. G. (2013/14). How Good is Good Enough? Educational Leadership, 74(4), pp. 10-16. Retrieved from http://www.ascd.org/publications/educational-leadership/dec13/vol71/num04/How-Good-Is-Good-Enough%C2%A2.aspx