From the Algebra I section of the Mathematics Framework for California Public Schools: Kindergarten Through Grade Twelve:
“Modeling problems have an element of being genuine problems, in the sense that students care about answering the question under consideration. In modeling, mathematics is used as a tool to answer questions that students really want answered. Students examine a problem and formulate a mathematical model (an equation, table, graph, etc.), compute an answer or rewrite their expression to reveal new information, interpret and validate the results, and report out. This is a new approach for many teachers and may be challenging to implement, but the effort should show students that mathematics is relevant to their lives. From a pedagogical perspective, modeling gives a concrete basis from which to abstract the mathematics and often serves to motivate students to become independent learners.”
(I can’t be sure, but the above passage sounds as if it were written by Phil Daro.)
I’ve seen this “make math relevant” and “problems that students really want answered” line of reasoning before from those who supposedly know what’s best for students. Out of the other sides of their mouths, they lament that math is not just about computation and push for problems that explore the relationship between perimeter and area of polygons and other concepts. Using the same logic about making math relevant one could then argue that students may not find such topics relevant to their lives. But people in the edu-establishment often have things both ways.
Extending this Phil Daro-ish logic that students only like to solve problems they really want answered, one would conclude that students do crossword puzzles and sudokus, because they really care about having them answered. Also breakout video games, Tetris and D&D.
In my experience and the experience of teachers who actually know what math is about and how to teach it, students care about problems if they’re able to solve them. Otherwise they write them off as irrelevant–sour grapes.
The problems that so-called math ed experts believe are so fascinating to students are generally one-off open-ended type problems which often involve gadgetry and ultimately number crunching. The fact that they don’t generalize to anything useful mathematically matters little to the people who write these frameworks.
3 thoughts on “Having it Both Ways, Dept.”
Here is the first paragraph.
“The main purpose of Algebra I is to develop students’
fluency with linear, quadratic, and exponential
functions. The critical areas of instruction involve
deepening and extending students’ understanding of linear
and exponential relationships by comparing and contrasting
those relationships and by applying linear models to data
that exhibit a linear trend. In addition, students engage in
methods for analyzing, solving, and using exponential and
quadratic functions. Some of the overarching elements of
the Algebra I course include the notion of function, solving
equations, rates of change and growth patterns, graphs as
representations of functions, and modeling.”
“Develop fluency” – Not ensure mastery
“Deepening and extending understanding ” – No fixed targets here.
“Engage in methods” – No fixed targets here.
“In modeling, mathematics is used as a tool to answer questions that students really want answered.”
That’s a self-serving Ed-School made up definition of modeling.
“This is a new approach for many teachers and may be challenging to implement, but the effort should show students that mathematics is relevant to their lives.”
That is arrant nonsense.
The problem is that we attempt to carefully address piffle like this while they just ignore our criticism because students and parents have no choice. That’s their greatest fear – choice.
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Reblogged this on Nonpartisan Education Group.
Interesting you posted this as I was reviewing some pre-AP materials for this fall. In case you didn’t know, the College Board has gone full constructivist, except when you actually take the AP Calculus or Stats exams. But I digress.
Anyway, what caught my attention is that the first topic in the Linear Equations and Linear Functions unit (Unit 1) is direct variation. And with their “model lesson plans,” it should only take you about 4 45-minute lessons to get them to figure out what direct variation is! Yes, you read that correctly. 180 minutes – THREE HOURS – to understand the concept. And of course, these lessons are all focused around “problems kids want to solve,” like how your speedometer shows mph and kph, and how they are related.
Of course there is no actual basic algebra I in this course; I suppose you master solving one-variable equations in Math 8 Common Core. This should be a very interesting year with the “pre-AP” class.