5 ms·

Honestly, the part that shocks me is that these are grade 8 tests (especially the math one). I knew that the US was lagging 1-2 years behind the rest of the wo

Honestly, the part that shocks me is that these are grade 8 tests (especially the math one). I knew that the US was lagging 1-2 years behind the rest of the world in mathematics [1] (also, from personal experience). The above isn't a math test, it is a kiddie pool. Where elsewhere in the developed world students are expected to do proofs at this age (even if they are simple ones), this test checks memorized knowledge by multiple choice. (Seriously, none of my teachers in secondary school would have been caught dead doing a single multiple choice question.) Please explain with specifics how to "teach to the test" in a manner that doesn't increase student knowledge. There's a difference between rote knowledge and understanding. I mean, seriously: Asking what a trinomial is (multiple choice, too, so you can guess pretty well) or calculating the area of a rectangle in eighth grade??? [1] http://parentsacrossamerica.org/james-milgram-on-the-new-core-curriculum-standards-in-math/ http://parentsacrossamerica.org/james-milgram-on-the-new-cor...

yummyfajitas 13y ago
There's a difference between rote knowledge and understanding. You didn't answer the question: how would you make scores on these tests go up without also making understanding go up (i.e. "teach to the test")? I'm now convinced that "teaching to the test" is likely a myth - not a single proponent of the idea has actually explained how to do it. (Incidentally, I'm not sure why you think the test I linked to is based on memorization. What would you memorize to make your score go up?) We might be giving a 6th grade test to the 8th grade - that's a flaw of the curriculum, not of the test.
- rbehrends 13y ago
  It's not just a curriculum issue. There are fundamental differences between math education in the US and math education elsewhere, which is where the curriculum issue comes from. As part of the 1998 TIMSS, a couple hundred videos were made of math teaching in the US, Germany, and Japan. James W. Stigler and James Hiebert then wrote a book, "The Teaching Gap: Best Ideas from the World's Teachers for Improving Education in the Classroom", on the content of these videos. They observed: "When we watched a lesson from another country, we suddenly saw something different. Now we were struck by the similarity among the U.S. lessons and by how different they were from the other country’s lesson. When we watched a Japanese lesson, for example, we noticed that the teacher presents a problem to the students without first demonstrating how to solve the problem. We realized that U.S. teachers almost never do this, and now we saw that a feature we hardly noticed before is perhaps one of the most important features of U.S. lessons - that the teacher almost always demonstrates a procedure for solving problems before assigning them to students. This is the value of cross-cultural comparisons." "For example, presenting a problem in Germany sets stage for a rather long development of a solution procedure, a whole-class activity, guided by the teacher. In Japan, presenting a problem sets the stage for students to work, individually or in groups, on developing solution procedures. In the United States, presenting a problem is the context for demonstrating a procedure and sets the stage for students practicing the procedure." Or, as a review of the book on Amazon summarizes: "In Japan, mathematics teaching is a method that aims to develop students' understanding of mathematical relationships and properties. This system of mathematical knowledge is taught to children in lessons that are highly coherent, hierarchically linear, and based on teachers' own research of what lessons promote student learning. Further, these lessons typically involve "structured problem-solving," where math concepts are induced from challenging problems, where these concepts are concretized through well-considered examples, and where mathematical relationships are proven as following necessarily from given premises. "In contrast, mathematics teaching in the U.S. seeks to train students in mathematical procedures. These procedures are taught to students by demonstrating one correct procedure for solving an easy problem, and then students are asked to imitate that procedure for many highly similar problems. More often than not, the lessons for imparting these skills are incoherent--with many non-mathematical discursions and interruptions. Further, lessons almost never involve math inductions and proofs; rather, teachers state math relationships explicitly and immediately tell students how the relationship should be used to solve simple problems. Last, lessons are developed by education researchers not only without the collaboration of teachers, but specifically so that the lessons are 'teacher-proof'." That's the difference: other countries teach problem solving and (deep) understanding. The US teaches simple, repeatable procedures. That's what then becomes "teaching to the test".
  - yummyfajitas 13y ago
    You didn't answer the question. If you were to "teach to the test" on any of the real tests I linked to, what simple repeatable procedures would you teach in order to make scores on those tests go up?
    - rbehrends 13y ago
      Have you actually looked at the test in question? For example, one question is basically knowing the definition of a trinomial, which is all about memorizing a definition, and has nothing to do with understanding the underlying mathematics. It's a problem of syntax and the meaning of a word, not semantics. Another requires calculating the area of a square by knowing to measure the lengths of the sides and multiplying them with each other. This is all about memorizing a set of procedures and applying them. Contrast that with this German question for 7th/8th graders: http://www.joerg-rudolf.lehrer.belwue.de/j3/images/mathe_sek/m8/Kongruenzbeweis6.pdf http://www.joerg-rudolf.lehrer.belwue.de/j3/images/mathe_sek... You're required to show that the quadrilateral IJKL is a square if the distances AE, BF, CG, and DH are of equal length, for which you have to show that all sides of IJKL are of equal length and that the angles of IJKL are all right angles. This requires a number of substeps, since you'll be reducing the problem to the question of congruences between triangles. More importantly, the point is not the difficulty of the question but that the question requires application of knowledge to a novel situation that the student hasn't encountered before (known as "transfer of learning" [1]), whereas US math problems tend to be carefully tailored to be straightforward applications for the memorized procedures. To the point that it is known that US math tests tend to eschew even word problems [2] to a great degree. Nobody says that "teaching to the test" doesn't teach students anything. The problem is that it teaches them procedures that require a minimum of independent thinking and are more about following down an established path. [1] http://edutechwiki.unige.ch/en/Transfer_of_learning http://edutechwiki.unige.ch/en/Transfer_of_learning [2] http://en.wikipedia.org/wiki/Word_problem_(mathematics_education) http://en.wikipedia.org/wiki/Word_problem_(mathematics_educa...
      - yummyfajitas 13y ago
        Are you asserting that to "teach to the test", you'd force students to memorize definitions, a couple of mechanical procedures (solve for x, simplify the expression) and drill formulas for the area of a circle and square into their heads, while ignoring understanding and the ability to apply it? The test had about 8 problems (out of 27) that are amenable to memorizing algebraic transformations or definitions. So "teaching to the test" as you describe it is a great way to make sure your students get a solid 30%. To the point that it is known that US math tests tend to eschew even word problems [2] to a great degree. There are about 8/27 word problems. The rest are geometric reasoning problems along the lines of the German test you link to (I don't read German so I can't compare except in general terms). Incidentally, transfer of learning is pretty much nonexistent. Wish I had an online source, but all I have to link to is a dead tree: http://www.amazon.com/Transfer-Learning-Instruction-Educational-Psychology/dp/0123305950 http://www.amazon.com/Transfer-Learning-Instruction-Educatio... Incidentally, I'm really glad someone is actually engaging with the topic rather than just reciting memorized talking points. Reminds me of what hacker news used to be like.

yummyfajitas 13y ago

There's a difference between rote knowledge and understanding. You didn't answer the question: how would you make scores on these tests go up without also making understanding go up (i.e. "teach to the test")? I'm now convinced that "teaching to the test" is likely a myth - not a single proponent of the idea has actually explained how to do it. (Incidentally, I'm not sure why you think the test I linked to is based on memorization. What would you memorize to make your score go up?) We might be giving a 6th grade test to the 8th grade - that's a flaw of the curriculum, not of the test.

rbehrends 13y ago
It's not just a curriculum issue. There are fundamental differences between math education in the US and math education elsewhere, which is where the curriculum issue comes from. As part of the 1998 TIMSS, a couple hundred videos were made of math teaching in the US, Germany, and Japan. James W. Stigler and James Hiebert then wrote a book, "The Teaching Gap: Best Ideas from the World's Teachers for Improving Education in the Classroom", on the content of these videos. They observed: "When we watched a lesson from another country, we suddenly saw something different. Now we were struck by the similarity among the U.S. lessons and by how different they were from the other country’s lesson. When we watched a Japanese lesson, for example, we noticed that the teacher presents a problem to the students without first demonstrating how to solve the problem. We realized that U.S. teachers almost never do this, and now we saw that a feature we hardly noticed before is perhaps one of the most important features of U.S. lessons - that the teacher almost always demonstrates a procedure for solving problems before assigning them to students. This is the value of cross-cultural comparisons." "For example, presenting a problem in Germany sets stage for a rather long development of a solution procedure, a whole-class activity, guided by the teacher. In Japan, presenting a problem sets the stage for students to work, individually or in groups, on developing solution procedures. In the United States, presenting a problem is the context for demonstrating a procedure and sets the stage for students practicing the procedure." Or, as a review of the book on Amazon summarizes: "In Japan, mathematics teaching is a method that aims to develop students' understanding of mathematical relationships and properties. This system of mathematical knowledge is taught to children in lessons that are highly coherent, hierarchically linear, and based on teachers' own research of what lessons promote student learning. Further, these lessons typically involve "structured problem-solving," where math concepts are induced from challenging problems, where these concepts are concretized through well-considered examples, and where mathematical relationships are proven as following necessarily from given premises. "In contrast, mathematics teaching in the U.S. seeks to train students in mathematical procedures. These procedures are taught to students by demonstrating one correct procedure for solving an easy problem, and then students are asked to imitate that procedure for many highly similar problems. More often than not, the lessons for imparting these skills are incoherent--with many non-mathematical discursions and interruptions. Further, lessons almost never involve math inductions and proofs; rather, teachers state math relationships explicitly and immediately tell students how the relationship should be used to solve simple problems. Last, lessons are developed by education researchers not only without the collaboration of teachers, but specifically so that the lessons are 'teacher-proof'." That's the difference: other countries teach problem solving and (deep) understanding. The US teaches simple, repeatable procedures. That's what then becomes "teaching to the test".
- yummyfajitas 13y ago
  You didn't answer the question. If you were to "teach to the test" on any of the real tests I linked to, what simple repeatable procedures would you teach in order to make scores on those tests go up?
  - rbehrends 13y ago
    Have you actually looked at the test in question? For example, one question is basically knowing the definition of a trinomial, which is all about memorizing a definition, and has nothing to do with understanding the underlying mathematics. It's a problem of syntax and the meaning of a word, not semantics. Another requires calculating the area of a square by knowing to measure the lengths of the sides and multiplying them with each other. This is all about memorizing a set of procedures and applying them. Contrast that with this German question for 7th/8th graders: http://www.joerg-rudolf.lehrer.belwue.de/j3/images/mathe_sek/m8/Kongruenzbeweis6.pdf http://www.joerg-rudolf.lehrer.belwue.de/j3/images/mathe_sek... You're required to show that the quadrilateral IJKL is a square if the distances AE, BF, CG, and DH are of equal length, for which you have to show that all sides of IJKL are of equal length and that the angles of IJKL are all right angles. This requires a number of substeps, since you'll be reducing the problem to the question of congruences between triangles. More importantly, the point is not the difficulty of the question but that the question requires application of knowledge to a novel situation that the student hasn't encountered before (known as "transfer of learning" [1]), whereas US math problems tend to be carefully tailored to be straightforward applications for the memorized procedures. To the point that it is known that US math tests tend to eschew even word problems [2] to a great degree. Nobody says that "teaching to the test" doesn't teach students anything. The problem is that it teaches them procedures that require a minimum of independent thinking and are more about following down an established path. [1] http://edutechwiki.unige.ch/en/Transfer_of_learning http://edutechwiki.unige.ch/en/Transfer_of_learning [2] http://en.wikipedia.org/wiki/Word_problem_(mathematics_education) http://en.wikipedia.org/wiki/Word_problem_(mathematics_educa...
    - yummyfajitas 13y ago
      Are you asserting that to "teach to the test", you'd force students to memorize definitions, a couple of mechanical procedures (solve for x, simplify the expression) and drill formulas for the area of a circle and square into their heads, while ignoring understanding and the ability to apply it? The test had about 8 problems (out of 27) that are amenable to memorizing algebraic transformations or definitions. So "teaching to the test" as you describe it is a great way to make sure your students get a solid 30%. To the point that it is known that US math tests tend to eschew even word problems [2] to a great degree. There are about 8/27 word problems. The rest are geometric reasoning problems along the lines of the German test you link to (I don't read German so I can't compare except in general terms). Incidentally, transfer of learning is pretty much nonexistent. Wish I had an online source, but all I have to link to is a dead tree: http://www.amazon.com/Transfer-Learning-Instruction-Educational-Psychology/dp/0123305950 http://www.amazon.com/Transfer-Learning-Instruction-Educatio... Incidentally, I'm really glad someone is actually engaging with the topic rather than just reciting memorized talking points. Reminds me of what hacker news used to be like.