17 votes

Different Teaching Styles for Different Genders?

I can't cite research to back me up on this, and you will want answers that reference research. But. Most of the differences between groups of boys and groups of girls come from how they've been ...
Sue VanHattum's user avatar
  • 20.3k
13 votes
Accepted

What is the correlation between students' contentment and educational quality?

From Clark, Richard, Paul A. Kirschner, and John Sweller. "Putting students on the path to learning: The case for fully guided instruction." (2012): Even more disturbing is evidence that when ...
Daniel R. Collins's user avatar
13 votes
Accepted

What does the research say about direct instruction vs. student centered approaches

Abstract from Alfieri, Brooks, Aldrich, "Does Discovery-Based Instruction Enhance Learning?", Journal of Educational Psychology, 2011: Discovery learning approaches to education have recently come ...
Daniel R. Collins's user avatar
13 votes

Teaching Calculus I to engineers

Without directly answering your question, you don't seem to have the background you need to be "improving" the undergraduate experience yet, and have some work to do. I think you're right in sensing ...
Scott Seidman's user avatar
12 votes
Accepted

Is there a literature database like MathSciNet for Mathematics Education?

Yes, there is one called MathEduc. Quote: MathEduc (formerly MATHDI) is the only international reference database offering a world-wide overview of literature on research, theory and practice in ...
Dag Oskar Madsen's user avatar
10 votes

Teaching Calculus I to engineers

Given 100% control, I would have one-to-one instruction. One instructor meeting individually with each student. That instructor can change the approach, the speed, the order of topics, the method of ...
Gerald Edgar's user avatar
  • 7,587
9 votes
Accepted

What are "PreK‐12th‐grade students"?

From the article: Grade level was a categorical factor consisting of three levels: preschool–kindergarten students (or its equivalent if outside of the United States), 1st‐ to 6th‐grade students, ...
user5402's user avatar
  • 1,528
9 votes

Math Education for Students who use Right-to-Left Written Languages

I have some personal experience. I taught in a school that has Israeli students whose families had moved to the US. These children had Hebrew as their native language. Hebrew is written right to left. ...
Amy B's user avatar
  • 8,017
9 votes
Accepted

Is there a widely respected early childhood math curriculum?

Yes. Most importantly, math in the early years should be play. My publisher has a lovely book titled Moebius Noodles that might give you more insight. But I wouldn't recommend anything like a ...
Sue VanHattum's user avatar
  • 20.3k
9 votes
Accepted

Where can I find new types of problems regarding graduate level mathematics?

As per my information , standard books from renowned authors and publications are the only sources of problems but still I want to know some sources where I can get difficult problems which can be ...
Justin Skycak's user avatar
9 votes

Where can I find new types of problems regarding graduate level mathematics?

Nowadays, you will be able to find many research mathematicians' websites with lecture notes for advanced courses, many with exercises/examples, many with solutions/discussions. I myself certainly put ...
paul garrett's user avatar
  • 14.6k
8 votes

"Function" vs "Function of ...": how much does it contribute to students difficulties?

I really appreciate your question. It gets to something I think about often when teaching calculus. You should read about Ed Dubinsky's notion of reflective abstraction, rooted in Piaget. At one ...
user52817's user avatar
  • 10.8k
7 votes

Reason behind the dominance of particular countries in the IMO (International Mathematical Olympiad)

The book by Masha Gessen on Grigory Perelman has a fascinating description of the Russian math camps, specialized schools (e.g., Specialized Mathematics School Number 239 in Leningrad), and the ...
Joseph O'Rourke's user avatar
7 votes

Different Teaching Styles for Different Genders?

I think the cognitive science is quite clear on this: Teachers should focus on learner similarities, not differences. Teaching to What Students Have in Common The corollary to the author's first "...
WeCanLearnAnything's user avatar
6 votes

Average time to solve basic arithmetic problem

This question is almost totally unanswerable unless you clarify what is meant by "basic arithmetic problems for kids and teens". But let's consider a lower-bound case where you're talking about ...
Daniel R. Collins's user avatar
6 votes

Is the education system in Finland particularly good?

The following research paper, by a Finnish researcher, is expressing more concern than enthusiasm about the effectiveness of the "Finnish way" to education: http://elib.mi.sanu.ac.rs/files/journals/...
Nicola Ciccoli's user avatar
6 votes

Propositional and predicate logic, with quantifiers: Is there any research when it is ideal to explicitly teach in mathematics education?

I'm afraid I don't know of any research that has been done to my satisfaction on this pedagogical issue of teaching logic, because all of those that I found so far (over many years) investigate ...
user21820's user avatar
  • 2,578
6 votes
Accepted

Policy in mathematics teaching

I will answer. I might not be answering the question asked (it is too unclear for me to be sure), but my answer is to what I think is being addressed in the linked book. (And if this question gets ...
Sue VanHattum's user avatar
  • 20.3k
6 votes

Importance of etymological approach to terminology

I think etymology is not useful in the way proposed by the OP. But here is a case in mathematics where etymology can help with spelling: parallelepiped The etymological analysis is: parallel + epi + ...
Gerald Edgar's user avatar
  • 7,587
5 votes
Accepted

"Function" vs "Function of ...": how much does it contribute to students difficulties?

Pat Thompson has done research on students' and teachers' understandings of functions and variation. (He's a co-author on the article mentioned in this answer, though he's not listed for some reason ...
Justin Hancock's user avatar
5 votes

conceptual framework

A conceptual framework should inform the experimental design, not be something that you add on like a garnish after the entire experiment has been planned. You say that the students are having ...
mweiss's user avatar
  • 17.4k
5 votes

Is there a framework to study the mathematical competence in problem-posing?

The answer to your question is yes. Check out the recent textbook: Singer, F. M., Ellerton, N. F., & Cai, J. (Eds.). (2015). Mathematical problem posing: From research to effective practice. ...
Benjamin Dickman's user avatar
5 votes

Source for analysis of identification of structures in learner's mind and mathematical structures?

This is not on general New Math controversy but more on Piaget. I suggest reading a few articles in general about issues with his assertions. Here is a simple overview, but several more are ...
guest's user avatar
  • 67
5 votes

Is there a study that proves that math proficients usually perform better in other subjects vs. people who perform shoddily in math?

"Other subjects" is a gross generalisation and it certainly is wrong to say that proficiency in mathematics correlates with proficiency in ALL other subjects. Numerous studies have focused on ...
yathish's user avatar
  • 536
5 votes

How to overcome the frustration in teaching and doing research at the same time

I think there's a lot of variability in publishing rates between different STEM fields and this can lead to administrators imposing unrealistic demands on Mathematics faculty. Anecdotally I've heard ...
Aeryk's user avatar
  • 8,011
5 votes

Teaching Calculus I to engineers

It's about the learning experience. An issue with project based learning is the need for objective grading isn't going away. Since the first semester of mathematics is what serves to filter out under ...
candied_orange's user avatar
5 votes

Adult Learners Returning to College Level Math

In the Encyclopedia of Mathematics Education. Lerman, Stephen, ed. Dordrecht: Springer, 2014. there is an article entitled "Adults Learning Mathematics" by Diana Coben and John O’Donoghue (...
Joseph O'Rourke's user avatar
5 votes

Cognitive activation vs cognitive load reduction

Here's the way I think about it: The purpose of cognitive activation is to get students to think deeply about what they're learning so that they incorporate it into their mental "tree of ...
Justin Skycak's user avatar
4 votes

Importance of exercises for learning mathematics

From my own experiences as a undergrad math major, I would say that good, quality exercises are one of the best tools for teaching math to people. Paul Halmos was right: "The only way to learn ...
Justin Benfield's user avatar
4 votes
Accepted

References on the effectiveness of manipulatives (virtual vs. physical)

Here's a piece comparing virtual manipulatives to traditional teaching without manipulatives, in the context of community college remedial courses: Violeta Menil and Eric Fuchs, "Teaching Pre-...
Daniel R. Collins's user avatar

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