Teacher Discussion:
2016 Alabama Course of Study: Mathematics Standards
Below is a list of standards and concepts that I identified as being relevant to how I solved the problem detailed in my project.
- Grade 7 #9, Solve multistep real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form, convert between forms as appropriate, and assess the reasonableness of answers using mental computation and estimation strategies. [7-EE3]
- Grade 8 #14, Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x,y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of linear function in terms of the situation it models and in terms of its graph or a table of values. [8-F4] Grade 7 #9, Solve multistep real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form, convert between forms as appropriate, and assess the reasonableness of answers using mental computation and estimation strategies. [7-EE3]
- Number and Quantity, Quantities, Reason quantitatively and use units to solve problems. [N-Q]
- Algebra, Seeing Structure in Expressions, Interpret the structure of expressions. [A-SSE]
- Algebra, Seeing Structure in Expressions, Write expressions in equivalent forms to solve problems [A-SSE] (Alabama State Dept. of Education, 2016)
This problem is a great example of both a high demand task that relates procedures to mathematical connections. It’s a problem that requires a lot of cognitive effort on the part of the students in order to answer the questions appropriately (National Council of Teachers of Mathematics, 2014, 18). It requires both an intimate understanding of the mathematics as well as how the mathematics relates to the context of the problem. For example, in problem 2, part a, students are asked to compare the new sequence they found with the previous ones they created from problem 1. This requires students to have a solid enough understanding of the sequences they crafted in order to identify the subtle details between them. Then students have to then take those mathematical differences and see how they relate to the real-world context of the problem. Another factor that made it a high level task was in being able to use mathematical action technologies in order to represent the problem in a different way, which helped students develop a better understanding of the mathematics behind the models they were creating (National Council of Teachers of Mathematics, 2014, 18).
I also like this problem because it was a great example of how to use a mathematical action technology in the classroom in order to promote student learning. A mathematical action technology is a described as a technological tool that can perform mathematical tasks and respond to the user’s actions in mathematically defined ways (Dick & Hollebrands, 2011, xii). For this problem, using spreadsheets served as a great example of how to use a mathematical action technology in a meaningful way. For example, the greatest strength of using spreadsheets for real-world contexts problems is the ease in which students can model and visually see patterns and changes depending on the sequences and formulas they craft to fit the real-world problems. Being able to easily change values and sequences highlights insights that would be much harder to discover using traditional paper and pencil methods. As a result, it has become easier for teachers to ask questions that promote a relational understanding of the material rather than being forced to ask more instrumental ones (Dick & Hollebrands, 2011, xvi). This problem that we analyzed in this project is a great example of that in that all of the questions posed by the problem are ones that ask for students to have a deeper understanding of the mathematics behind the problem in order to answer. Rather than asking what a value is at a certain point, the problem asks students to problem solve and reason by asking students to compare and contrast sequences and explain what those differences mean in the context of the problem.
References
Alabama Course of Study: Mathematics. Alabama State Dept. of Education, 2016.
Dick, T. P., & Hollebrands, K. F. (2011). Focus in high school mathematics: Technology to Support Reasoning and Sense Making. Reston, VA: National Council of Teachers of Mathematics.
National Council of Teachers of Mathematics. (2014). Principles to actions: Ensuring mathematical success for all. Reston, VA: Author.
Morrell Math Corner 