Working with Common Core

Deconstruction of a Standard
Abstract
The purpose of this deconstruction of a standard exercise was to unpack a standard, examine it critically and identify the key words to help determine the level of cognitive demand (based on Bloom’s Taxonomy). A review of the standard as a whole was conducted to identify the type of achievement target. The standard selected was the 9th Grade Mathematics Common Core Standard CCSS.MATH.CONTENT.HSS.IC.A.1. The achievement target for the standard was understanding (comprehension) and therefore the lesson targets focused on weighting the different cognitive demands according to the place in the process of understanding at which they occurred. This paper provides a Deconstructing a Standard Table and a Reflection of the process overall—including my reaction to the process, identification of specific professional development that may be needed in my building, and my role as a leader.
Keywords: common core standards, math standards, understanding 9th grade math
Background/introduction to the table
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 that is recommended for all levels. It applies to the content standard stated above because it illustrates how the content is to be understood—i.e., through practice and application of the learning.
The table below describes the content standard identified in this paper, the learning targets, and the level of cognitive demand that the student must demonstrate. The student must show the ability to remember, understand, apply and analyze. The first learning targets focus on remembering and they have the lowest weighting because the student is just starting out. The middle learning target has a higher weighting because the student is expected to be able to draw on prior knowledge and demonstrate understanding at this point. The student is thus challenged to return to his notes, recall and recollect the meanings and definitions so that he can show understanding. Then it comes time to apply the learning, which follows understanding: understanding cannot really be measured unless the student applies the knowledge to an actual problem. This learning target is thus weighted the same as the understanding target. Finally there is the analyze aspect, in which the student is required to explain in words the meaning of the problem and how to solve it. This has the highest weighting as it is the culmination of everything that has come before.
Reflection
The content standard—“Understand statistics as a process for making inferences about population parameters based on a random sample from that population”—is based on the student’s need to be able to comprehend statistics in the math course. The student has to be able to show 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 (Bloom’s Taxonomy also contains affective and sensory domains). The cognitive domain includes: 1) knowledge (remembrance), 2) understanding (comprehension), 3) application (the ability to use the understanding in a problem-solving manner, 4) analysis (the ability to explain what happened and why), 5) synthesis (the ability to bring all the information together to create new understanding, and 6) evaluation (the ability to measure one’s performance). For this lesson, areas 1-4 of the cognitive domain were covered and the fifth and sixth areas were excluded—primarily because the lesson was not being combined with any other so there was no room for synthesis and the evaluation process would come later after multiple lessons had allowed for a proper synthesis to be achieved (Bloom, 1956).
My reaction to the process was that overall breaking down the standard into learning targets according to Bloom’s Taxonomy of the cognitive domain was a very helpful way to go about teaching the standard and getting students to move through it at a good pace. The students were first tasked with acquiring the knowledge and remembering the basic ideas of the standard. Then they had to begin to demonstrate understanding and the ability to apply their understanding. After that occurred, I was able to ask them to explain and analyze using their understanding. This was an agreeable process that could be replicated again easily using Bloom’s Taxonomy.
Specific professional development that may be needed in my building would be regarding an explanation of the cognitive demands as well as a possible exploration of how to tie in the other two domains of Bloom’s Taxonomy—the sensory and affective domains. Could math and other disciplines be better supported by making full use of Bloom’s Taxonomy? Our building could likely benefit from an exploration of this question and some discussion of whether it could be the case that combining the cognitive with the affective and sensory would help students reach the standards even more effectively.
In my role as a leader, I would like to bring these topics forward and demonstrate the success I have had using Bloom’s Taxonomy as this Deconstructing a Standard template to help prepare a lesson and present it to the class. As I believe this is an effective way of preparing the lessons—by identifying the targets and weighting them accordingly—I think others would likely benefit from this as well. I would seek to promote this approach in my building by bringing up the discussion question and presenting my information from my own personal experience and challenging others to follow suit.
Conclusion
In 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 the lesson targeting practices. I found that as a leader I would like to promote this use of Bloom’s Taxonomy and find ways to bring all the domains together—cognitive, sensory and affective—so as to fully help students acquired 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
http://www.corestandards.org/Math/Content/HSS/IC/
Common Core Standards for Mathematical Practice. (2019). Standards for Mathematics.
Retrieved from http://www.corestandards.org/Math/Practice/
Introduction to Statistics. (2018). What is statistics? Retrieved from
https://slideplayer.com/slide/6137045/