Wednesday, January 20, 2016

Is this the best NYSED can do? (Turkey continued..)

Print Friendly and PDF The "commentary" following the problem referred to in How do you cook a turkey? (my blog post from yesterday) states the following (page 27 here):
This question measures A-CED.A because students must create an exponential
equation and use it to solve problems.
I beg to differ: the exponential equation is not created by the student, but handed to them and credited to Newton.

Once it is recognized that this problem does NOT address the part of the common core standards it claims to, its reason for existence in this setting is gone.

This problem is connected to "Mathematical Practice(s) 1 and 4 (see page 27 here).  Mathematics practice 1 is stated here (italics are mine):

MP 1 - Make sense of problems and persevere in solving them.
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. They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary. Older students might, depending on the context of the problem, transform algebraic expressions or change the viewing window on their graphing calculator to get the information they need. Mathematically proficient students can explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends. Younger students might rely on using concrete objects or pictures to help conceptualize and solve a problem. Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, “Does this make sense?” They can understand the approaches of others to solving complex problems and identify correspondences between different approaches. 

This problem expects students to jump in and attempt a solution using the equation they are given.

Mathematical practice 4 is here:
MP 4 - Model with mathematics.
Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. In early grades, this might be as simple as writing an addition equation to describe a situation. In middle grades, a student might apply proportional reasoning to plan a school event or analyze a problem in the community. By high school, a student might use geometry to solve a design problem or use a function to describe how one quantity of interest depends on another. Mathematically proficient students who can apply what they know are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later. They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas. They can analyze those relationships mathematically to draw conclusions. They routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose.
This problem expects, almost requires, that the student do no modelling whatsoever. The modelling has already been done by Isaac Newton.

Come on NYSED, fix this.

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