Deconstructing a 9th Grade Math Common Core Standard

Introduction and Standard Background

The standard selected for this paper was the 9th Grade Mathematics Common Core Standard CCSS.MATH.CONTENT.HSS.IC.A.1: "Understand statistics as a process for making inferences about population parameters based on a random sample from that population" (Common Core, 2019). The Common Core Standards for Mathematical Practice states that "mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt" (Common Core Standards for Mathematical Practice, 2019). This is the practice standard recommended for all levels.

The Mathematical Practice standard applies to the content standard identified above because it illustrates how the content is to be understood—that is, through practice and application of the learning. The achievement target for this standard was determined to be understanding (comprehension), and the lesson targets were therefore structured to weight different cognitive demands according to the stage of understanding at which they occur.

Learning Targets and Cognitive Demand

The table accompanying this paper describes the content standard, the learning targets, and the level of cognitive demand the student must demonstrate. Students must show the ability to remember, understand, apply, and analyze. The first learning targets focus on remembering and carry the lowest weighting because the student is just beginning to engage with the material. The middle learning target carries a higher weighting because the student is expected to draw on prior knowledge and demonstrate understanding at this stage. The student is challenged to return to notes, recall definitions, and show comprehension of the material.

It then becomes necessary to apply the learning, which follows naturally from understanding: understanding cannot truly be measured unless the student applies knowledge to an actual problem. This learning target is therefore weighted the same as the understanding target. Finally, the analyze component requires the student to explain in words the meaning of the problem and how to solve it. This carries the highest weighting, as it represents the culmination of everything that has come before.

Reflection on the Deconstruction Process

The content standard—"Understand statistics as a process for making inferences about population parameters based on a random sample from that population"—is grounded in the student's need to comprehend statistics within the math course. The student must demonstrate that "statistics is a way of reasoning, along with a collection of tools and methods, designed to help us understand the world. Statistics are particular calculations made from data" (Introduction to Statistics, 2018).

Using Bloom's Taxonomy, most educators focus on the cognitive aspects of development, though Bloom's Taxonomy also encompasses affective and sensory domains. The cognitive domain includes: (1) knowledge (remembrance), (2) understanding (comprehension), (3) application (the ability to use understanding in a problem-solving manner), (4) analysis (the ability to explain what happened and why), (5) synthesis (the ability to bring all information together to create new understanding), and (6) evaluation (the ability to measure one's own performance). For this lesson, levels one through four of the cognitive domain were addressed. The fifth and sixth levels were excluded primarily because the lesson was not combined with others, leaving no opportunity for synthesis; evaluation would come later, after multiple lessons had enabled a proper synthesis to be achieved (Bloom, 1956).

The overall reaction to the process was positive. Breaking down the standard into learning targets according to Bloom's cognitive domain proved to be a very useful approach for teaching the standard and moving students through it at a productive pace. Students were first tasked with acquiring knowledge and remembering the basic concepts of the standard. They then began to demonstrate understanding and the ability to apply what they had learned. Once that occurred, students were asked to explain and analyze using their understanding. This was an effective and replicable process that can be revisited easily using Bloom's Taxonomy as the organizing framework.

Conclusion

This exercise was a helpful one in terms of being able to unpack a standard, clarify its meaning, identify the learning targets, weight them appropriately, and find ways to bring the lesson to completion through the management of lesson targeting practices. The process confirmed that identifying and weighting learning targets through an established cognitive framework provides a sound basis for effective lesson design. As a leader, the intention is to promote the use of Bloom's Taxonomy and to explore ways to integrate all three domains—cognitive, sensory, and affective—so as to more fully support students in acquiring the standards.

References

Bloom, B. S. (1956). Taxonomy of educational objectives: The classification of educational goals. Handbook I: Cognitive domain. New York: David McKay Company.

Common Core. (2019). Standards. Retrieved from

Common Core Standards for Mathematical Practice. (2019). Standards for Mathematics. Retrieved from

Introduction to Statistics. (2018). What is statistics? Retrieved from https://slideplayer.com/slide/6137045/