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In mathematics education, it has always been a struggle for me to utilize the upper levels of Bloom’s Taxonomy. In my early years of learning and teaching, there seemed to be a major focus on the lower levels, and not much emphasis on the upper levels. Writing in mathematics was almost non-existent. In fact, most of my current students question the practice of writing complete sentences in math assignments, even if current texts provide opportunities to do so. The expectation of my students is to provide numerical responses, along with necessary “showing work”, but the idea of writing or providing other levels of processes in Bloom’s Taxonomy is considered extraneous and superfluous.
Fortunately, most current textbook publishers provide teachers with resources to provide great opportunities to utilize all the levels in practice problems, traditional assessments, and performance assessments. For example:
A teacher gives a test to a class of 25 students. The grades are as follows: 40% of students receive a grade of C (test scores of 70% to 79%), 40% of students receive a grade of either B (80% to 89%) or D (60% to 69%), 20% of students receive a grade of either A (90% to 100%) or F (0% to 59%).
a) Write a set of 25 test scores based on the information above.
b) From your data, determine the mean, median, and mode for the class.
c) Draw a graph that properly displays your data.
Demonstrate your knowledge by designing a water tower tank with the following requirements. The height of the water tank must be 30 feet. The horizontal tank dimensions must cover as much as possible of the 70-foot by 70-foot plot of land that the tower will sit on. The tank must have a volume of at least 90,000 cubic feet and not more than 100,000 cubic feet. The potential choices for the shape of the tank are cone, cylinder, pyramid, prism, sphere, and hemisphere.
1. On a separate sheet of paper, draw each figure based on the height and land requirements. Label the dimensions for each.
2. Based on the requirements in Exercise 1, find the volume for each figure to the nearest cubic foot.
3. Describe any shortcuts you could take in finding the volumes.
4. Which shapes meet the water tower tank volume requirements? Explain how the figures in Exercise 1 can be modified to fit the tank’s volume requirements. Describe the new dimensions and volume for each to the nearest tenth cubic foot.
These examples show that they ask students more than just remember or understand processes.
The National Council of Teachers of Mathematics (NCTM) has encouraged this higher level thinking as well. Mathematical modeling has been a strategy to teach meaningful learning of mathematics content. It is “a process that uses mathematics to represent, analyze, make predictions or otherwise provide insight into real-world phenomena” (Hernandez et al., 2017). It has been a struggle for high school math teachers like me to implement this type of learning process. Hernandez describes how you can introduce this mathematical modeling in your class. (2017)
- Start small
- Scaffold initial experiences with leading questions and class discussion
- Use common, everyday experiences to motivate the use of mathematics
- Use bite-sized modeling scenarios that require only one or two components of a full modeling cycle
- Share your goals and instructional practices with parents and administrators
I think it would benefit all students as they learn math content to be provided real-world problems to solve. Many math texts, in my opinion, provide what I call story problems for the sake of making a story problem, which is not real-world. The issue is that in order to solve real-world problems, students need a full skill set of math tools, strategies, and content to do this, which usually is encountered later in their secondary math career. It is the goal of all math teachers to provide students with mathematical modeling opportunities to solve problems that will arise in their lifetime and hopefully make a difference.
Assessment Resources. (n.d.). Holt Geometry. Holt, Rinehart and Winston – A Harcourt Education Company. Page 200
Data Analysis and Probability – All-In-One Teaching Resources Chapter 12. (n.d.) Prentice Hall Algebra 1- Teaching Resources. Page 89.
Hernandez, Maria L.; Levy, Rachel; Felton-Koestler, Mathew D.; Zbiek, Rose Mary. (2017). Mathematical Modeling in the High School Curriculum. Mathematics Teacher. Vol. 110, No. 5.
Thomas, Douglas; Seely Brown, John. A New Culture of Learning: Cultivating the Imagination for a World of Constant Change (Kindle). CreateSpace. Kindle Edition.