Talk:Math Maturity
From IAE-Pedia
Comment by Bob Stein 8/1/2010
The following is quoted from an email message sent by Bob Stein to David Moursund:
- … I reread your issue on mathematical maturity. It raised another issue, which I feel is germane to both the use of history and to the larger questions of how we teach.
- I refer specifically to the idea of teaching for understanding. We often say that is what we want, but we rarely define what it is, because we rarely pay much attention to what understanding really is. I can address that issue only in subjective terms.
- For me, understanding involves connections. When I learn something, be it a fact, a technique, or whatever, in isolation, I cannot possibly understand it. When I connect that fact or technique to the web of knowledge that I already have in my mind, it takes on what I call (and what feels to me like) meaning.
- From that point of view, putting history into a math course can only enrich the web of connections that the student builds, both between mathematical ideas and between mathematical ideas and other ideas.
- As to whether students enjoy history in a math course: In general, they certainly do. For some, it is more fun than math, but most simply like to see that this stuff was thought up by real people in real situations.
Comment by James Miller 3/6/2010
To me, math maturity is demonstrated by students willing to take any math problem and trying to develop a solution and by showing a joy in this process. It is demonstrated by students having the basics of math that is gained from grade school through college, and obtained by having teachers that have a joy for math and can share it with students.
Comment by Dick Ricketts 11/9/2009
People professionally adept at mathematics, who can understand and create original work, can be termed “mathematically mature.” More generally, people who are adept at dealing with mathematical aspects of their lives also can be termed “mathematically mature.” “Mathematical aspects” includes aspects amenable to rational analysis.
Mature people have the attitudes, knowledge, and skills—grounded in experience—to deal responsibly the problems, situations, and tasks that occur in their cultures or societies and cultures. Mature people act appropriately, adaptively, and rationally. (This does not exclude the possibility of standing one’s ground.) In this sense, children can be mature. Persons become mature through formal learning, through observations, and through personal experience.
For professional educators, these definitions means that math education has a three-fold task: Enabling all students deal with mathematical situations they currently encounter and will encounter as adults, enabling some students who will use “more advanced’ math as a tool, and encouraging those few who embrace professional mathematics. It implies that an educator should be able to give a real-world explanation to any students ask why they are studying this: It’s part of every well-educated person’s equipment, it’s essential to the vocation one may be interested in, or it’s something the student will enjoy.
Comment by David Moursund 10/6/09
Revising the Math Maturity Web Page has proven to be a very challenging task. And, the overall topic deserves still more and better supportive materials. It is beginning to look to me like the project needs to become a book writing project. It is also clear to me that lots and lots more examples are needed. HELP!!!
Comment by Dick Ricketts 7/19/09
I continue to think that "What questions would you ask an adult to assess math maturity?" will prove useful. What should one expect the average adult, with recard to math, be able to take in (rad etc.) and produce? What use of conscious logic and mathematical tools do people use in everyday lives, or even on infrequent occasions?
Thought up a quote: Math is a recreation, a scaffolding, and a tool.
Is math maturity a subset? Maybe.
Math maturity is emotional, intellectual, and social maturity with respect to logic, numbers, and patterns.
Comment by Joseph Dalin 6/14/09
The following email message sent to David Moursund was in response to a email message about math and Talented & Gifted education sent to an National Council of Supervisors of Mathematics distribution list.
- Hi,
- The major question is: what is a [sic]Talented and Gifted persons or students? What is his/her special capabilities? Memorizing or the capability of understanding? Do the Talented and Gifted students learn differently? Do they understand symbolic abstract language better, or significantly better, than ordinary students?
- The basic education of mathematical understanding and creative thinking is gained through solving problems of cases which deal within the child's environment, experience and conceptual system.
- Algebra is a symbolic abstract nonhuman language. In order to understand such a language there is a need to have a "mathematical thinking maturity” and than—to translate the symbolic representations into graphic representation and learn through self experience, exploration and discovery (which is the way human beings learn).
- It can be achieved by comprehensive integration of Visual-dynamic-quantitative computer software into the teaching and learning process of school mathematics.
- Such an approach should be applied for all students, not only Talented and Gifted students.
- I don’t believe that, in general, students of 5th grade have the “mathematical learning maturity” for learning algebra 1.
- I don’t believe that most students of 7th grade are capable to leaning algebra 1 through its symbolic representation only. Anyhow, what’s the rush? Learning is a long journey….
- I don’t believe that most students, even in higher grades, are capable to really understand Algebra by learning only through its symbolic representations. That’s the main reason of poor achievement, failure and frustration of school mathematics education which is based on teaching symbolic mathematics.
- I am ready to share my experience.
- Dr. Joseph Dalin, Director, Israeli Institute for the Integration of Computers in Mathematics Education.
Comment by Marsha Lilly 6/21/09
The following is from an email message sent to Moursund on 6/21/09:
- The best resources that I have worked with relating to building conceptual development in mathematics are the courses produced by Agile Mind – beginning with Grade 7 through and including the Calculus: http://www.agilemind.com.
Comment by ottoseitz 5/18/09
The following is quoted from an email message sent to the NCSM discussion list of speakers at the NCSM 2009 Annual Conference.
- My advanced students seem to be able to handle an amazing amount of abstraction related to that course [Algebra 2]. They are more tuned to algorithms but are able to extend their thinking. I suspect that their high level of engagement in learning is the reason.
- Now my average sophomore class is entirely different. They need a pretty careful level of development to get them to any abstractions. I'm convinced the average student needs to get a much more rigorous level of development of thinking. I'm afraid that average students get to do a lot more mechanical learning as they go through school.
Comment by David Moursund 5/4/09
The following is quoted from an email message sent to the NCSM discussion list of speakers at the NCSM 2009 Annual Conference.
- In recent years I have gotten interested in the general topic of math cognitive development. My "guess" that this is roughly the same topic as "math maturity."
- In the recent Algebra II discussion on the NCSM discussion list, the argument was used that a great many students at the high school level lack the math maturity (the Piagetian developmental) to effectively deal with and understand the abstractions in a moderately rigorous Algebra II course. I'd appreciate hearing people's insights, experiences, and links to relevant literature on this topic.
Comment by Clyde Greeno 4/9/09
The following is quoted from an email message sent by Clyde Greeno to the National Council of Supervisors of Mathematics distribution list on 4/9/09:
- The entrenched "developmental" algebra curriculum (like the HS algebra curriculum) is a direct decedent from SMSG's calculus-preparatory HS algebra—which has served more to filter students out of the mathematics curriculum than to empower them for success within it. [No wonder that educators now are concerned about the "Algebra 2 for everyone" movement among state legislatures.]
- Extensive clinical research has revealed that the primary cause for students' difficulties with algebra is simply that algebra curricula within the SMSG lineage badly violate scientifically established principles of the developmental psychology of mathematical learning—i.e. of "mathematics as common sense". [The original SMSG version was created two decades before America began to understand Piaget.] Ironically, the resulting "developmental" algebra curriculum is anything but developmental. The coming reformation will be guided by psychology.
- Clinical methods quickly reveal that students learn the usual essentials of algebra better, faster, and more easily through the context of functions. That is partly because the field of algebra really is all about the study of operations/functions—even the SMSG curriculum was covertly about functions—even though that context still is badly hidden by the current curriculum.
