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The question that I asked was related to Mathematical Maturity. If you try to search the literature in Mathematics Education for Mathematical Maturity you will not find much. Of course you will find the Wikipedia page and a few blogs related to it, but not many research papers. In fact, I only know of an article named Developing Mathematical Maturity by Lynn Steen (1983) in: The Future of College Mathematics (pp. 99-110). Springer, New York, NY. But the topic is important enough that Terrence Tao and Bill Thurston have written about it. While the phrase Mathematical Maturity does not directly appear in their writings, one can argue that Tao's blog post There is more to mathematics than rigour and proofs and Thurston's On proof and progress in Mathematics address Mathematical Maturity, among other things.

While there is no universal definition for Mathematical Maturity, mathematicians have been using the phrase. The situation reminds me of notions such as naturality or moduli space that were used by mathematicians before they had a formal definition. In the case of naturality, MacLane and Eilenberg captured its definition by introducing the notion of natural transformations of functors. So being able to provide a universally agreeable definition of Mathematical Maturity is a research level question in Mathematical Education, although, that was not what my post was about. Another challenge is to have tools for measuring the development of Mathematical Maturity from Pre-Calculus to Calculus III. But who can address these questions about Mathematical Maturity? I would like to argue that one has to be a mathematician to know what Mathematical Maturity means. Terrence Tao would know more about Mathematical Maturity. Bill Thurston would know more about Mathematical Maturity. Mathematicians are the ones who know about Mathematical Maturity. And this is why my question is not more appropriate for Stack Exchange Mathematics Educators, but appropriate for Mathoverflow, for mathematicians to respond to it (of course, only if the topic interests them). To my point, I recommend reading the report How Do Mathematicians Describe Mathematical Maturity? by Kristen Lew, who is a mathematics educator. What do mathematics educators do when they want to research Mathematical Maturity? They interview mathematicians!! Interestingly, she found that none of the four applied mathematicians whom she interviewed had used or knew of the phrase Mathematical Maturity.

The question that I asked was related to Mathematical Maturity. If you try to search the literature in Mathematics Education for Mathematical Maturity you will not find much. Of course you will find the Wikipedia page and a few blogs related to it, but not many research papers. In fact, I only know of an article named Developing Mathematical Maturity by Lynn Steen (1983) in: The Future of College Mathematics (pp. 99-110), Springer, New York, NY. But the topic is important enough that Terrence Tao and Bill Thurston have written about it. While the phrase Mathematical Maturity does not directly appear in their writings, one can argue that Tao's blog post There is more to mathematics than rigour and proofs and Thurston's On proof and progress in Mathematics address Mathematical Maturity, among other things.

While there is no universal definition for Mathematical Maturity, mathematicians have been using the phrase. The situation reminds me of notions such as naturality or moduli space that were used by mathematicians before they had a formal definition. In the case of naturality, MacLane and Eilenberg captured its definition by introducing the notion of natural transformations of functors. Therefore, being able to provide a universally agreeable definition of Mathematical Maturity is a research level question in Mathematical Education, although, that was not what my post was about. Another challenge is to have tools for measuring the development of Mathematical Maturity from Pre-Calculus to Calculus III. But who can address these questions about Mathematical Maturity? I would like to argue that one has to be a mathematician to know what Mathematical Maturity means. Terrence Tao would know more about Mathematical Maturity. Bill Thurston would know more about Mathematical Maturity. Mathematicians are the ones who know about Mathematical Maturity. And this is why my question is not more appropriate for Stack Exchange Mathematics Educators, but appropriate for Mathoverflow, for mathematicians to respond to it (of course, only if the topic interests them). To my point, I recommend reading the report How Do Mathematicians Describe Mathematical Maturity? by Kristen Lew, who is a mathematics educator. What do mathematics educators do when they want to research Mathematical Maturity? They interview mathematicians!! Interestingly, she found that none of the four applied mathematicians whom she interviewed had used or knew of the phrase Mathematical Maturity.

Yesterday I posted a question tagged Mathematics Education. It was quickly closed. It was judged to be more appropriate for Stack Exchange Mathematics Educators. One person commented that it was not a research level question. Another person started acting out and making irrelevant and off topic comments. Interestingly, nobody attempted to answer the question itself! These people did not have any knowledge on the topic of the question. In fact, the topic is a research level question in Mathematics Education and the very fact that someone says it is not, shows they have no information about the topic. I like to assume that if a question does not interest someone, they can just skip it without feeling any urge for making hasty comments under the question.

Yesterday I posted a question tagged Mathematics Education. It was quickly closed. It was judged to be more appropriate for Stack Exchange Mathematics Educators. One person commented that it was not a research level question. Another person started acting up and making irrelevant and off topic comments. Interestingly, nobody attempted to answer the question itself! These people did not have any knowledge on the topic of the question. In fact, the topic is a research level question in Mathematics Education and the very fact that someone says it is not, shows they have no information about the topic. I like to assume that if a question does not interest someone, they can just skip it without feeling any urge for making hasty comments under the question.

Why is Mathematical Maturity important? We often expect our Calculus III students to be "better" than Pre-Calculus students in learning mathematics. One can argue that by "better" we mean mathematically more mature. Consequently, one way to see whether our Pre-Calculus to Calculus III sequence is working properly or not, is to look at students' development of Mathematical Maturity from Pre-Calculus to Calculus III. Of course, one may say if students passed their Calculus courses, it means they learned, so why do we need to monitor their development of Mathematical Maturity? But those of you who know something about teaching Calculus, know that just because students pass a course doesn't mean they learned it. I submit that a successful Calculus program is one that develops students' Mathematical Maturity by as much as possible.

Why is Mathematical Maturity important? We often expect our Calculus III students to be "better" than our Pre-Calculus students in learning mathematics. One can argue that by "better" we mean mathematically more mature. Consequently, one way to see whether our Pre-Calculus to Calculus III sequence is working properly or not, is to look at students' development of Mathematical Maturity from Pre-Calculus to Calculus III. Of course, one may say if students passed their Calculus courses, it means they learned, so why do we need to monitor their development of Mathematical Maturity? But those of you who know something about teaching Calculus, know that just because students pass a course doesn't mean they learned it. I submit that a successful Calculus program is one that develops students' Mathematical Maturity by as much as possible.