Respect the Struggle

In IBL classes, being stuck is a critically important part of the experience for students.  One of the greatest lessons a student can learn in school is how to manage being stuck.

One of the issues we face, particularly in the U.S., is that mistakes are stigmatized, and this context makes teaching problem solving more difficult.  When a student gets a problem wrong it is far too often interpreted as a criticism of their mathematical ability.  Yet, in contrast to this problem-solving ability and creative thinking are highly regarded attributes in all areas of life.

What can we do as teachers?  Students must know that

It's okay to be stuck!

In fact, being stuck is a noble state.  It's when we are stuck that we learn to learn. It's when we are stuck that we construct new ideas, and discard or improve upon ones that are not good enough for our current situation.  Being stuck is good!

One facet of effective teaching is respecting the struggle.  What this means is to allow students to struggle and think, in such a way that they are not stressed out, rushed, or feel that making mistakes is "bad."  Ensuring that students feel that they are allowed to explore, think, experiment, and build ideas that may not work is critical to building a positive learning environment.

Giving away answers or letting students flounder excessively are two ways we can get off track.  As a teacher one should monitor students and manage the struggle so that students are challenged, making progress (over time), and not overly frustrated.

How do you know if you have a positive learning environment in your classroom?  Ask yourself if your students feel it's okay to be stuck.

"We Are In the Business of Transforming Lives!" -- Mike Starbird

As the fall term approaches, I hear as clear as ever Mike Starbird's words, "We are in the business of transforming lives!"   It's important to remind ourselves that we are not just teaching algebra or calculus.  We are using mathematics as a vehicle to help students find their mathematical talent.  We are nurturers of talent, not machines created show students how to plug in numbers or solve for $x$.

When I think of the fall term and my classes, I also think about how I can help create more opportunities for students to transform themselves, their self image in math, and how they go about learning and doing math.  Before diving into all of the details of building up a syllabus and deciding how much this or that, the beginning of the academic year is an opportunity for teachers to revisit the reasons why we teach and what the point of education is.

Cheers from SLO!

"Thank you for treating us like professionals"

This week I had the pleasure of working with San Luis Coastal Unified School District math teachers.  My colleagues Linda Patton, Marian Robbins, and Elsa Medina did a fantastic job of running sessions specially designed for K-12 math teachers.  The teachers were inspired to think, to problem solve, to work together, and to think of ways to get their students to do some real mathematics.  It was a great 3-day workshop, and I am looking forward to the follow-up days in the coming year.

On the last day of the workshop, one of the teachers said, "Thank you for treating us like professionals."  The teachers were kind, energetic, wonderful to work with, and highly appreciative of the support we provided.  They accomplished a great amount in a short time.  But this workshop experience, where teachers feel like professionals and are treated as such, is not the norm.  It is a strange thing that such a circumstance could even exist in the U.S.  The fact that society has evolved to make teachers feel marginalized, despite their importance to society and our future, is astonishing.

In future posts, I'll dive into some of the ideas of why this issue is really a signal for a larger set of problems in education reform.  That is, how society treats, supports, and values teachers in society leads to key insights.

For college faculty, what all this probably means is that the (relatively) easy part of the whole enterprise is to teach future teachers the math (or fill-in your subject).  

The Colorado Study: The Vectors Are All Pointing in the Same Direction

Sandra Laursen, Marja-Liisa Hassi, Marina Kogan, Anne-Barrie Hunter, at the University of Colorado Ethnography & Evaluation Research and Tim Weston, ATLAS Assessment and Research Center University of Colorado Boulder have conducted a large, mixed-method study of IBL at 4 research universities in the U.S.  This is the largest study of its kind, and the results are striking.  (Link to the study)

What did they learn?

• LESS instructor talk time, results in BETTER outcomes.
• Women in IBL classes reported as high or higher gains than their male classmates across all cognitive, affective and social gains areas (3.2.3). But women in non-IBL classes reported statistically much lower gains than their male classmates in several important domains: understanding concepts, thinking and problem-solving, confidence, and positive attitude toward mathematics.
• Among students who entered with low math GPAs (<2.5), IBL students generally earned better grades in later classes than did their non-IBL peers (6.4.1).
• Attitudinal changes were modestly positive in IBL groups, and mixed and somewhat negative in non-IBL groups.  Overall, IBL math courses tended to promote slightly more sophisticated and expert-like views of mathematics and more interactive approaches to learning. In contrast, traditional mathematics courses appeared to weaken students’ confidence and enjoyment, and did not help them to develop expert-like views or skillful practices for studying college mathematics.

The overall results of the Colorado study points in the same direction as the bulk of the results from the Math Education literature.  When students are (a) deeply engaged in high quality mathematical tasks requiring critical thinking and reasoning, and (b) have some form of collaboration, then student outcome are statistically significantly better compared to students in a non-IBL setting.  (Collaboration is broadly defined here.  Collaboration is not only group work, but includes activities such as class discussion and student presentations to the whole class.  In this last instance, the class is peer-reviewing the presenter's work.  This is collaboration.)

When the Colorado study is combined with the literature from Math Education, then we start to put together a rather clear picture.  We have known already that students have historically had poor attitudes and beliefs about Math from K-college.  Students have beliefs such as "all problems can be solved in 5-minutes or less" and "it's the form of the answer that important, not the quality of the process or content of the proof."

We also know that students, even college students, have limited ability in problem solving and proof.  Students are rarely exposed to the kinds of experiences necessary to develop problem solving, the critical thinking and reasoning for proof, and other higher-level thinking strategies.  High stakes testing and the drive for further standardization has made it more difficult for students to develop the kinds of attitudes and thinking skills needed to learn math beyond rote skill.  

In light of this, the Colorado study shows that IBL methods (broadly defined) is a glimmer of hope.  When students are given a chance to think for themselves and are properly supported by the instructor and their peers, that students are capable of rising up and fulfill their potential.

The data speaks -- all the vectors are pointing in towards IBL.

IBL User Experience: Kyle Peterson

Kyle Peterson is a Professor of Mathematics at DePaul University.


Let $n$ be an integer greater than one. Since $n$ and its successor,
$n+1$, are relatively prime, their product, call it $n_2 = n(n+1)$,
has at least two distinct prime factors. By similar reasoning, the
product of $n_2$ and its successor, say $n_3 = n_2(n_2+1)$, has at
least three distinct prime factors. Continuing in this way, we can
construct, for any positive integer $i$, a number with at least $i$
distinct prime factors. Hence the set of primes is not finite.

Not a bad little argument, eh? It's my favorite proof of the
infinitude of the primes, and I first read it on the homework turned
in by one of my students, whom I'll call Sara. If you are a regular
reader of American Mathematical Monthly, you may remember this
argument from a note by Filip Saidak in the December 2006 issue, two
months after Sara handed in her homework.

Sara was an average student, certainly not the ``best" of the class. I
had expected her, like many of her classmates, to construct an
argument similar to Euclid's classic contradiction argument, since
that's what my carefully chosen sequence of problems pointed to. (Or
so I thought.) I remember being so floored by what I read in Sara's
paper that I initially thought there must be some error. It was so
different from what I was expecting to see! But no, it was correct,
and I immediately ran across the hall to share it with a friend.

This is the potential of an IBL class. Given only the necessary
preliminaries, along with some time and space to think, Sara had come
up with something truly novel. It was just a month or so into my first
semester of IBL teaching, and, like the hack golfer who hits a
hole-in-one, I was hooked. I had never had a student so thoroughly
surprise me, and I wanted to experience more of those surprises.

I've been teaching IBL for about five years now, and while a gem of
that magnitude is rare, I find smaller surprises happen on a regular
basis in my IBL courses. For one thing, just because a student comes
up with a proof, the way they arrive at the proof often takes its own,
fascinating path. Other sorts of surprises include the time a student
who doesn't seem to be paying attention pipes up to point out a flaw
the rest of the class missed. Or when a student who would rather die
than go to the board in the first few weeks leaps out of her chair to
go to the board in the last few weeks. People laughing and smiling...
in a math class! Rather than: What do I have to talk about today?, I
walk into the room thinking: What will the kids show me today?

My favorite overheard conversation last year:

Student 1: ``So I think we have a bijection. Do we have a bijection?"
Student 2: ``I don't know...(mumble, mumble)... Wait! Yes!"
Student 1: ``We do?"
Student 2: ``Yes!"
Student 1: ``Yes!"
-Slap!- (the students give each other a high five)

Not every IBL course will necessarily produce a revelation like Sara's
proof, but they all produce everyday miracles that will delight and
surprise you. Using a lecture-only format pretty much guarantees that
your students won't surprise you, since they will be doing
their best to mimic what you do. To paraphrase something I've often
heard Ed Parker say: Why should we limit our students to what we know?

Classroom Strategy: Think Pair Share

One of the most effective and easiest ways to get students involved in your classroom is to use Think Pair Share.  Harvard Professor and Physicist, Eric Mazur, has been one of the strongest proponents of using peer instruction.

How does Think Pair Share work in a mathematics classroom?  It goes like this...

• Pose a question or task to the class, such as "Give an example of..." or "Which ones of these, if any, is an example of...?"
• (Think) Let students think about the question/task individually for about a minute (or whatever appropriate time) 
• (Pair) Ask students to explain their solution/idea/thoughts to one person sitting next to them.
• (Share) Involve the entire class in a discussion of the question/task.  A good way to start off is to walk around the class while the pairs are discussing and ask one or two pairs to share their ideas.
• (Recycle) If necessary, a class may not arrive at a consensus.  In such cases the class can re-enter the pair phase and work with their partner to sort out the details.

Below are some examples chosen from elementary Number Theory.  But these ideas can be easily adapted to any math course from Calculus to Math for Elementary Teaching to Real Analysis.

Example1:  (Starter question)

• State the definition of $n|k$, where $n,k$ are integers.
• Question: In your own words, interpret what $n|k$ means.  Write a few sentences.
• Share with your neighbor your sentences and revise if necessary.
• Pick a few groups to share their work.

Example 2:

• Task: Determine which of the following statements is true.  
1. If $n$ is even, then $2|n$.
2. If $n$ is even, then $n|2$.
• Think for yourself which one is correct.
• Convince your neighbor of your answer.
• Class discussion. Recycle if there is confusion or lack of consensus.  

Example 3:

• Question: If $n|a$ and $n|b$, then $n|(a+b)$.
• Think of some strategies you could use to prove this theorem
• Discuss your strategies with your neighbor.  Write questions, if you have any.
• Pick a few groups to share their strategies and/or questions
• Make a list of the ideas, and let students continue to ask questions.  Then one can move on to the next task, leaving the proof as a homework problem that will be shared later.  Another option is to let students come up with a sketch of a proof in class and clean it up at home to be turned in/presented the next time.

Why IBL? The Road to Present Day IBL

By Amélie G. Schinck

(Originally posted on the AIBL website)

Inquiry-Based Learning (IBL) is not a recent or passing movement in mathematics education. IBL is based on a wide body of research and has a long track record of success. The following is an outline of IBL’s theoretical background and empirical grounding.

At the university level, IBL is also known as the Modified Moore Method (MMM), named after professor R. L. Moore of the University of Texas. In the majority of undergraduate mathematics classrooms across the nation, “doing mathematics means following the rules laid down by the teacher; knowing mathematics means remembering and applying the correct rules when the teacher asks a question; and mathematical truth is determined when the answer is ratified by the teacher” (Lampert, 1988, p.437). Moore aimed to challenge students’ assumptions about what it is to do, know, and understand mathematics. Beginning in the 1920’s, and continuing for half a century, Moore taught collegiate mathematics through inquiry, challenging his students to think like mathematicians. Moore believed: “That student is taught the best who is told the least” (Parker, 2005, p.vii). Through a sequence of carefully crafted problems and theorems, Moore would have students pose conjectures, construct their own proofs, justify their reasoning to their peers at the board, and assess the validity of proposed solutions and proofs. Textbooks were generally not used. Lectures were kept to a minimum. Collaboration between classmates was strictly prohibited. For a biography of R. L. Moore, and an account of the origin and impact of the Moore Method, see Zitarelli (2004) and Whyburn (1970). For more information on R. L. Moore, also see http://legacyrlmoore.org.

The Modified Moore Method is a less strict version of Moore’s approach to the teaching and learning of mathematics. For instance, MMM courses may make use of an IBL inspired textbook. Varying degrees of importance can be placed on formal examinations. Student collaboration is sometimes encouraged, with solutions to problems shared during small-group and/or whole-group discussions. For descriptions of different modifications and their rationale, see Chalice (1995), Mahavier (1999), and Padraig & McLoughlin, (2008). For some examples of IBL textbooks, see Burger & Starbird (2005), Hale (2003), Schumacher (1995) and Starbird, Marshall & Odell (2007). For refereed, IBL classroom tested course notes for university level mathematics classes, visit the website for the Journal of Inquiry-Based Learning in Mathematics (www.jiblm.org).

Students are thus engaged in the creation of mathematics, allowing them to see mathematics as a part of human activity, not apart from it. MMM courses are in direct contrast to the traditional lecture-based approach to the teaching of mathematics. Reporting on his use of MMM, Chalice (1995) stated:

While using this method, I have been able to cover as much material (and in few cases more material) as in the usual lecture-style course. More importantly, with the Modified Moore Method, the students and I have covered that material in a far more enlivening, enjoyable, and intellectually stimulating way (p.317).

An inquiry-based approach was recommended by the National Science Foundation in their 1996 report of a year-long review of the state of undergraduate Science, Mathematics, Engineeringand Technology (SME&T) education in the United States entitled Shaping the Future (NSF, 1996). In this report, the researchers stated that it is imperative that:

All students have access to supportive, excellent undergraduate education in science, mathematics, engineering, and technology, and all students learn these subjects by direct experience with the methods and processes of inquiry (NSF, 1996, p.6).

The IBL movement found in undergraduate mathematics, and supported by the Academy of Inquiry-Based Learning (AIBL), is in line with, and a natural extension of, the reform efforts in grades K-12. Recommendations by the National Council of Teachers of Mathematics (NCTM) for the past three decades (NCTM, 1980, 1989, 2000) have consistently included a call for a focus on teaching problem solving by teachers, positioning problem solving ability as the overarching goal of mathematics education. These recommendations are founded on the notion that the learning of mathematics is an active, social process in which students construct new ideas or concepts based on their current knowledge. Student understanding is connected to open- ended questions and an inductive teaching style. Principles and Standards for School Mathematics (NCTM, 2000) emphasizes the need for teachers to create a culture of learning in their classroom in which students learn with understanding and construct conceptual mathematical meaning through a problem-solving approach:

Problem solving means engaging in a task for which the solution is not known in advance. In order to find a solution, students must draw on their knowledge, and through this process, they will often develop new mathematical understanding. Solving problems is not only a goal of learning mathematics but also a major means of doing so. (NCTM, 2000, p.51)

Discussing the importance of fostering Reasoning and Proof in Grades 9-12, Principles and Standards for School Mathematics (NCTM, 2000) states:

As in other grades, teachers of mathematics in high school should strive to create a climate of discussing, questioning, and listening in their classes. Teachers should expect their students to seek, formulate, and critique explanations so that classes become communities of inquiry (p.346).
To sustain and support the recommended focus on problem solving, active learning and inquiry in grades K-12, undergraduate mathematics education must also change, especially in the area of teacher preparation (NSF, 1996).

As mathematics education researchers turn their attention to IBL, evidence is mounting that this approach to the teaching of mathematics is ideal for the teaching of proof (e.g. Smith, 2005; Dhaler, 2008). Despite the emphasis on proof in higher level undergraduate mathematics courses, research on students’ conception of proof consistently shows that most struggle with appreciating, understanding and producing mathematical proof (Dreyfus, 1999; Harel & Sowder, 1998; Jones, 2000; Selden & Selden, 1987, 2003; Weber, 2001). Many mathematics educators argue that students’ (mis)conceptions about proof are the inevitable result of the traditional, lecture-based approach to the teaching of proof (Dreyfus, 1999; Harel & Sowder, 1998; Jones, 2000; NCRTL, 1993; Shoenfeld, 1988; Silver, 1994; Smith, 2005). In his article Why Johnny can’t prove, Dreyfus (1999) noted that “the ability to prove depends on forms of knowledge to which students are rarely if ever exposed” (p.85). Dreyfus (1999) concluded that a classroom environment in which students are required to explain and justify their reasoning is key to helping students transition from a computational view of mathematics to a view that conceives of mathematics as a field of intricately related structures.

Smith (2005) reports on the results of an exploratory study of the perceptions of mathematical proof and strategies for constructing proof of undergraduate students enrolled in lecture-based and problem-based (MMM) “transition to proof/number theory” course. Smith (2005) found evidence that the problem-based approach provided students with more opportunities to make sense of the proof construction process in a personally meaningful way than the lecture-based approach. Smith (2005) noted marked differences between the two groups of students. For instance, students in the lecture-based course focused on the form of the proof rather than on its meaning, and were reluctant to work concrete examples. On the other hand, students in the MMM course emphasized meaning over surface features, introduced notation in the sense-making process, conjured up previous proof strategies on the basis of the concept under study, and made use of concrete examples to gain insight into the main idea. Based on these results and the preliminary analysis of other collected data, Smith (2005) hypothesized that classroom communities of inquiry (such as MMM) encourage students to produce proofs by making global or intuitive observations about the mathematical concepts and transform these observations into formal, deductive reasoning.

In a dissertation study on the effects of the Modified Moore Method on college students’ concept of proof, Dhaler (2008) found that MMM had a positive effect on student’s conceptualization of mathematical proof, as well as on self-confidence in their abilities, their appreciation of the relevance of proof, and their ability to be independent thinkers.

An inquiry approach to teaching has also been shown to have a positive effect on students’ acquisition and retention of conceptual understanding. At the K-12 level, Boaler (1998), for instance, showed that students who learned mathematics in an open, project-based approach developed superior conceptual understanding to their counterparts who had learned the same subject matter through a traditional, textbook approach. A central part of Boaler’s study was to compare students’ capacity to use their mathematical knowledge in new and unusual situations. Boaler (1998) found that students who had been taught in the traditional way “did not think it was appropriate to try to think about what to do; they thought they had to remember a rule or method they had used in a situation that was similar” (p.47). On the other hand, students who had been taught in an open approach could use mathematics in novel situations as they had developed the belief that mathematics required active, flexible thought. Furthermore, they had gained the capability to adapt strategies and methods depending on the situation. Though the project-based approach described in Boaler (1998) is not identical to the inquiry-based learning approach sponsored by AIBL, the implications of Boaler’s study remain ; conceptual understanding is improved when students learn mathematics by engaging in inquiry.

At the undergraduate level, Rasmussen & Kwon (2007) provides a summary of two quantitative studies that assessed the effectiveness on student learning of an inquiry-based approach to the teaching of differential equations (as part of the Inquiry Oriented Differential Equations (IO-DE) project.) Rasmussen, Kwon, Allen, Marrongelle, and Burtch (2006) compared students that had taken inquiry-oriented differential equations (IO-DE) classes versus students that had been taught using a traditional approach. Rasmussen et al. (2006) found that although the two groups did not show a significant difference in procedural fluency (i.e. routine problems), the IO-DE group scored significantly higher on conceptual problems.

In a follow-up study one year later, Kwon, Rasmussen, and Allen (2005) compared the retention effect on procedural and conceptual understanding between the traditional and IO-DE group. The data showed no significant difference between the two groups in procedural fluency. However, the IO-DE group showed a significant positive difference compared to their traditional counterpart on conceptual understanding.

The IO-DE project described above uses an adaptation of Realistic Mathematics Education (RME), an inquiry approach to the teaching of K-12 mathematics in the Netherlands. RME is based on curriculum developed at the Freudenthal Institute. Through the posing of true problematic situations (not simply “word problems”), RME encourages student investigation and inquiry. Students’ construction and representation of mathematical concepts such as number sense is valued. The book series Young Mathematicians at Work by Fosnot and Dolk outline the translation of the Dutch approach to the teaching of mathematics to numerous American urban classrooms.

The famous Swiss psychologist Jean Piaget stated: “to understand is to invent”, highlighting the active nature of the learner. The above discussion provides an outline of the theoretical foundation on which Inquiry-Based Learning rests. Furthermore, it provides a summary of the mounting evidence that students who are given the opportunity to learn mathematics through inquiry develop deeper procedural and conceptual understanding of mathematics.

References

Boaler, J. (1998). Open and closed mathematics: Student experiences and understandings. Journal for Research in Mathematics Education, 29(1), 41-62.

Burger, E., & Starbird, M. (2005). The Heart of Mathematics: An Invitation to Effective Thinking, Emeryville,CA: Key College Publishing.

Chalice, D. R. (1997). How to teach a class by the Modified Moore Method. The American Mathematical Monthly, 102(4), 317-321.

Dhaler, Y. Y. (2008) The effect of a Modified Moore Method on conceptualization of proof among college student. Dissertation Abstracts International Section A: Humanities and Social Sciences, 68(11-A), 4591.

Dreyfus, T. (1999). Why Johnny can’t prove, Educational Studies in Mathematics, 38, 85-109. Hale, M. (2003). Essentials of mathematics: Introduction to theory, proof, and the

professional culture. Washington, DC: MAA.

Harel, G., & Sowder, L. (1998). Students’ proof schemes: Results from exploratory studies. In A. H. Schoenfeld, J. Kaput, & E. Dubinsky (Eds.), Research in Collegiate Mathematics Education III (Vol. 7, pp. 234-283). Providence, RI: American Mathematical Society.

Jones, K. (2000). The student experience of mathematical proof at university level. International Journal of Mathematical Education in Science and Technology, 31(1), 53-60.

Kwon, O.N., Rasmussen, C., & Allen, K. (2005). Students’ retention of mathematical knowledge and skills in differential equations. School Science and Mathematics, 105, 227-239.

Lampert, M. (1988). The teacher’s role in reinventing the meaning of mathematical knowing in the classroom, in Proceedings of the PME-NA, pp. 433-480.

Mahavier, W.S. (1999). What Is The Moore Method? Primus, 9(4), 339-354. Martin, G., & Harel, G. (1989). Proof frames of preservice elementary teachers, Journal for

Research in Mathematics Education, 20(1), 41-51. National Center for Research on Teacher Learning (1993). Findings on Learning to Teach, Lansing, MI: NCRTL.

National Science Foundation (1996). Shaping the future: New Expectations for Undergraduate Education in Science, Mathematics, Engineering, and Technology, Advisory Committee to the NSF Directorate for Education and Human Resources. Accessible at www.nsf.gov (file nsf96139)

National Council of Teachers of Mathematics (1980). An Agenda for Action: Recommendations for School Mathematics of the 1980s. Reston, VA.

National Council of Teachers of Mathematics (1989). Curriculum and Evaluation Standards for School Mathematics. Reston, VA.

National Council of Teachers of Mathematics (2000). Principles and Standards for School Mathematics.Reston, VA.

Parker, J. (2005), R. L. Moore: Mathematician and Teacher, Washington DC.: Mathematical Association of America.

Padraig, M, & McLoughlin, M. (2008). Inquiry Based Learning: A Modified Moore Method Approach To Encourage Student Research. Paper presented at the 11th Annual Legacy of R. L. Moore Conference, Austin, TX.

Rasmussen, C., & Kwon, O.N. (2007). An inquiry-oriented approach to undergraduate mathematics. Journal of Mathematical Behavior, 26, 189-194.

Rasmussen, C., Kwon, O. N., Allen, K., Marrongelle, K., & Burtch, M. (2006) Capitalizing on advances in mathematics and K-12 mathematics education in undergraduate mathematics: An inquiry-oriented approach to differential equations. Asia Pacific Education Review, 7(1), 85-93.

Schoenfeld, A. H. (1988). When good teaching leads to bad results: The disasters of “well- taught” mathematics courses. Educational Psychologist, 23, 145-166.

Schumacher, C. (1995). Chapter Zero; Fundamental notions of abstract algebra, Addison- Wesley Publishing Co.

Selden, A., & Selden, J. (1987). Errors and misconceptions in college level theorem proving. In J. D. Novak (Ed)., Proceedings of the second international seminar on misconceptions and educational strategies in science and mathematics (Vol III, pp. 457-470). Ithaca, NY: Cornell University.

Selden, A., & Selden, J. (2003). Validation of proofs considered as texts: Can undergraduates tell whether an argument proves a theorem? Journal for Research in Mathematics Education, 34, 4- 36.

Smith, J. C. (2005). A sense-making approach to proof: Strategies of students in traditional and problem-based number theory courses. Journal of Mathematical Behavior, 25, 73-90.

Starbird, M., Marshall, D., & Odell, E. (2007). Number theory through inquiry. DC: MAA textbooks.

Weber, K. (2001). Student difficulty in constructing proof: The need for strategic knowledge, Educational Studies in Mathematics, 48(1), 101-119.

Whyburn, L.S. (1970). Student oriented teaching – The Moore Method. The American Mathematical Monthly, 77, 351-359.

Zitarelli, D. E. (2004). The origin and early impact of the Moore Method. The American Mathematical Monthly, 111(6), 465-486.

New Blog About Teaching and Learning Mathematics

The IBL Blog will focus on inquiry-based learning in Mathematics.  The main focus will be college-level instruction, but all levels (K-college) will be discussed.  I'll have a lot of posts about general issues in Education, and I will encourage my colleagues to contribute.

About myself... My name is Stan Yoshinobu, and I am a Cal Poly Professor in Mathematics.  I am also the Director of the Academy of Inquiry Based Learning (www.inquirybasedlearning.org).  I am an advocate for using research-based teaching methods that involve students in the process of doing mathematics, rather than sitting on the sidelines watching someone else do it.   More than just better, inquiry-based learning can provide transformative experiences for students.  Those of us who teach are truly lucky -- we are in the business of transforming lives!

Blog posts will include the following topics

• Teaching ideas and tips for the classroom
• Experiences from the field written by guest or regular contributors
• Commentary on news articles and reports
• Essays on teaching and learning
• Resources for students, teachers, parents, staff, administrators
• Ideas, commentary and resources for people interested or involved with education policy

Look for lots of new regular content coming up!