The newspaper article explained that the math taught in Maryland high schools is deemed insufficient by many colleges. In many cases incoming college students cannot do basic arithmetic even after passing all the high school math tests. The problem appears to be worsening and students are unaware of their lack of math understanding.
The article reported that students are actually shocked when they are placed into remedial math. The article did not shock me. It described my observations exactly. In recent years I've witnessed first hand the disconnect between the high school and college math curricula. As a parent of three children with current ages 14, 17, and 20, I've done my share of tutoring for middle school and high school math and I know how little understanding is conveyed in those math classes.
Ironically much of the problem arises from a blind focus on raising math standards. For example, the problems assigned to my children have become progressively more difficult through the years to the point of being bizarre. My wife keeps shaking her head at how parents without my level of math expertise assist their children. My eighth-grade daughter asked me one evening how to perform matrix inversions. I teach matrix inversion in my sophomore-level mathematical methods course for physics majors.
It is difficult for me to do matrix inversions off the top of my head. I needed to refresh my memory by pulling Boas' book: Mathematical Methods in the Physical Sciences off my shelf. Not exactly eighth grade reading material. On another night my eighth-grader brought home a word problem that read: If John can complete the same work in 2 hours and that it takes Mary 5 hours to complete, how much time will it take to complete the work if John and Mary work together? That's an easy problem if you know about rate equations. Add the reciprocals of 2 and 5 and reciprocate back to get the total time.
However it took me a lot of thought to arrive at an explanation of my method comprehensible to an eighth-grader. My other daughter struggled through a high-school trigonometry course filled with problems that I might assign to my upper-class physics majors. I certainly wouldn't assign problems at such a high level to college freshmen.
I kept asking her how she was taught to do the problems. I wondered if the teacher knew special techniques unknown to me that made solving them much easier. Alas no such techniques ever materialized. The problems were as difficult as I judged. At least I could solve the problems, a feat the teacher couldn't manage in a number of cases.
For example one problem involved proving a complicated trigonometric identity. My daughter brought it to me saying she had tried but couldn't find a solution. I saw immediately that the textbook had an error that rendered the problem meaningless. One side of the problem had a combination of trigonometric functions with odd symmetry and for the other side the symmetry was clearly even. I told her it was not an identity and that fact could be proven with a simple numerical substitution on each side.
If it is an identity the equality condition must hold for all values of the angle. A single numerical counter example proves that it is not an identity. It only took one try to find a counter example. The next day she reported to me that the teacher couldn't solve the problem.
He didn't believe me. He just said 'We'll see'. He did teach the class about the symmetry properties of trigonometric functions but evidently he didn't understand the usefulness of that knowledge. At the same time I work the summer orientation sessions at Loyola College registering incoming freshmen for classes. Time and again students cannot pass the placement exam for college calculus.
Many students cannot pass the exam for pre-calculus and that saddles them with a non-credit remedial math course--the problem described in the newspaper article. Without the ability to take college-level math the choices students have for majors are severely limited. No college-level math course means not majoring in any of the sciences, engineering, computer, business, or social science programs. A colleague in the engineering department who also works summer orientation complained to me that many students who wanted to major in engineering could not place into calculus.
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The engineering program is structured so that no calculus means no physics freshman year and no physics means no engineering courses until it's too late to complete the program in four years. For all practical purposes readiness for calculus as an entering freshman determines choice of major and career. The math placement test given to incoming freshmen at orientation has much higher stakes than any test given in high school. The Journal of Educational Research, 71 2 , Wammes, J.
The drawing effect: Evidence for reliable and robust memory benefits in free recall. The Quarterly Journal of Experimental Psychology, 69 9. Wu, J. Using time pressure and note-taking to prevent digital distraction behavior and enhance online search performance: Perspectives from the load theory of attention and cognitive control.
Computers in Human Behavior, 88, Categories: Instruction , Learning Theory , Podcast. I have the same question. I teach gr 3 and am trying to think of ways to incorporate this into our class. This website is my go-to source for research-backed, teaching best-practice info. For example, we watched a video and I asked them to jot down what they noticed. Then I asked them to share what they had noticed and we made a mind map together, with students adding anything they had missed wherever they felt it fit best.
math matters a pedagogy of remediation Manual
What about 1st grade? Kids love to write and doodle, right? As a former 1st grade teacher, all throughout the day, I provided tons of opportunities for kids to record their thinking.
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They were writing, doodling, drawing arrows, labeling, captioning … doing all that stuff that we want them to do when showing understanding. Of course, this came with a lot of scaffolding, modeling, and direct teaching. I think sketchnoting is perhaps the most natural way to get kids started. I say it was all that and more. My real intention was to teach a learning process: 1.
Listen to just get familiar with the content.
Chapter 3 - Remedial Teaching Strategies
Listen again, this time really visualizing the content. Draw, write, label what you understand. Listen again and fix or change. The tool we used was a Scholastic News issue that happened to coincide with our weather unit. I read it aloud, one section at a time. Several note-taking strategies were part of this lesson: sketchnoting, revision, pausing, scaffolding, and shout-outs, which I considered a form of collaboration.
Not only could they do it, but they enjoyed it…and the learning really did stick. Hope this helps! I think there is definitely power in taking notes but does this actually look at deep understanding of a concept and application or retention and regurgitation?
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Would love to know your thoughts. On the other hand, without consuming actual information and ideas that have been put out into the world by others, students will be limited in how far their application can go. When I wanted to create a podcast, I watched a lot of YouTube videos and read a lot of articles that taught me how to do it. I took notes. Lots of them. Messy at first, but then I rewrote and reorganized them so they were more useful to me later. I watched some of the videos more than once and revised my notes. Then, as I practiced with all the technical elements of audio recording and editing, I referred back to those notes.
The learning was an interplay between intake, processing note-taking , and application. If any of those parts were missing, I think the learning would suffer.
Note-taking: A Research Roundup
Loved this. This is just amazing. I saw Daniel Willingham, a widely respected educational researcher, present on this topic a year or so ago. Enjoy, everyone! A very important issue in note taking is the distinction learning from taking notes and using notes to learn. These processes are distinct and very different issues can be important with each. If notes are not used for review, some learners would be better off note taking notes.
Note review does not necessarily depend on the learner taking notes. What a great resource on how to make note-taking an integral part of our classroom.
Related Math Matters: A Pedagogy of Remediation
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