Three months after the beginning of last school year I asked the students in my math classes to rate the experience so far in comparison to other math classes they have had, using a scale from one to ten, with one meaning it was “the worst ever” and ten meaning “the best ever.” Pretty simple.

I made it clear that the question wasn’t about how much they like math, or what they thought of me. I stressed that I wanted to get feedback on how well they felt this more independent style of learning was working for them. I did the same thing this year although the question was asked near the end of the year rather than at the beginning. The results are shown in the graphs below followed by a brief analysis and discussion.

Prealgebra Class Survey Results

Figure 1

Figure 2

The above histograms are for last year’s prealgebra classes (Figure 1) and this year’s (Figure 2). The axis scales are set up alike so the graphs are directly comparable to each other. Note that in 2011 (Figure 1) the pattern was somewhat bimodal with a quite a few kids stating they did not like being in a flipped class very much. But, there were even more that claimed they rather liked it. The mean rating for that year by 66 students was 6.3 with a standard deviation of about 3. Figure 2 from this year shows a clear shift to the right and indeed the mean rating is 6.9 with a standard deviation of about 2. So over all, the kids were more accepting of it this year. More on that later. Now for the same survey given to algebra students.

Algebra Class Survey Results

Figure 3

Figure 4

A can be seen from Figures 3 and 4 there was a major shift in attitude among the algebra learners. In 2011 slightly over half the class rated their experience above a 5. The mean for that year was 6.1 with an sd of 2.2. This year, no one rated the class below a 7 and the majority rated it at full 10. The mean this year was 9.1 and the sd was 1.2. Wow, what a difference.

Why so Much Better This Year?

Overall I am pleased with the improved attitudes toward the flipped class and acceptance of it by both students and parents this year. This year there have been a few polite concerns expressed but nothing compared to what we went through last year. I think there are a couple of reasons for this.

First of all, it wasn’t new this year. The word had gotten out, at least to some extent, and people in the school community knew what I was doing. As a result I know that one or two families requested I be their kid’s teacher, and I am sure at least that many requested I not be their teacher. Both of those situations are good as far as I am concerned. Schools should offer options and should not  be “one size fits all” institutions.

Secondly, the counseling department did an excellent job of evaluating the needs, background, and learning styles of the students before they were scheduled for classes this year. Counseling chose to assign kids to my classes that they felt would appreciate the method and I think that over all it worked. I hope they do the same for next year. Which is not to say I that it worked well for everyone. I am generally not satisfied with the progress that most of the learners made, especially in prealgebra.

My experience this year has given me a lot to think about and I already have some ideas for how to improve the flipped class for next year. Fortunately for me, there are two other flippers at Challenger now and we will work together to do what works, and replace what doesn’t.

In my flipped Algebra and Prealgeba 7 classes the learners work at their own pace and when they complete a learning assignment they show me what they’ve got. I periodically check to see that they are taking good notes and they have to show me their problem sets when they are complete before they go off to check their results themselves. I don’t check their work, they check their work. I guess you could say I check their checking of their work. Each of these presents an opportunity for one-to-one communication focused on the goal (which is not to “take notes” or “complete problem sets,” but to learn how to think mathematically and solve problems). As it turns out, each of these is an opportunity for effective praise.

What is Effective Praise?

For praise to be effective, it should reenforce the behavior you want to see more of. Statements like “good job,” or “well done” are okay but not highly effective. My thinking on the power of praise has been influenced by Daniel Pink in his book Drive, Alina Tugend’s Better by Mistake, Charle’s Murray’ Real Education (don’t shoot me) and Dan Ariely’s The Up Side of Irrationality.

Here are my guidelines for effective praise in the classroom:

• Don’t praise kids for being smart
• Praise the effort that leads to a good result, not the result itself
• Recognize sustained effort, even if the end result has not yet been achieved
• Be impressed by hard work, not right answers
• Praise something specific like “wow, the axes labels on that graph are perfectly spaced” not “nice graph.”

Sure it is okay to congratulate someone on getting a tough or interesting problem right, but wrap it in words that indicate that the effort it took to get there is what is really important.

The Flipped Class is Made for Effective Praise

Every time a learner shows me their work or we discuss their progress it presents an opportunity for effective praise. What is different about how this work in a flipped class is that the opportunities come to me, I don’t have to go looking for them. The opportunities are built into the system. Nothing cold be easier!

Retired U.S. Senator Ben Nighthorse Campbell

Ben Nighthorse Campbell represented Colorado in the United States Senate for twelve years (two terms) before retiring in 2005. Prior to that, he served six years (3 terms) in the U.S. House. He has remained active with the law firm Holland and Knight, and continues to travel and work toward improving the lives of Native Americans.

Campbell still puts in a 35-40 hour a week on average in his legal work, but the former senator considers himself equally as much a jeweler (“…my real life’s work”). Along with spending time with family, grandkids, and taking street rods to shows with whoever wants to ride along, Campbell puts in many hours a week of his own time, working on tribal issues and related legislation. Two areas that are of particular interest right now are health care reform and education.

Native American Healthcare and Healthcare Reform

Perhaps more than other citizens, Native Americans will probably be affected by whatever health care reform is eventually signed into law. They get much of their coverage from the Indian Health Service, which is underfunded and overused. There is also a lack of health care providers in Indian Country. Even though he thinks there is a lot to be gained from reform, Campbell is not convinced that any of the reforms under discussion offer the best solution.

“I am not a fan of the current healthcare reform bills. It is an enormously costly way to address the issue. There are cheaper and more effective ways to address getting access to quality health care to those citizens who do not have health care without excess government involvement.”

The former republican senator still values that conservative mainstay: less government. “Government has never proven to be a good provider of any services for the money spent. There are ways to address this without turning the system on its ear or spending a trillion dollars by allowing small businesses to band together as risk groups to avail themselves to private insurance options and then providing incentives to insurers to provide affordable coverage to those who remain.”

Campbell has some ideas for improvement. “We need to provide more incentives for health care providers to work in Indian Country, in all of rural America for that matter. Reauthorization of the Indian Health Care Improvement Act would be a good step. But we also need more a preventive health care focus and more outside-the-box thinking in Indian health care.”

Native American Education

Campbell says he believes that education is better today in Indian Country than it was in the past. “Many of the wealthier tribes are in urban areas and their kids have access to better public schools. Other successful tribes, dissatisfied with their public schools or the Bureau of Indian Affairs (BIA) system have started their own school districts and brought in top-flight educators.”

Campbell adds, “Now, the reality is that the successful tribes make up only 10-12% of Indian Country. The other 90% face a different reality. The BIA system has gotten better through the years, but it is grossly underfunded.”

Simply increasing funding to the current system is unlikely to be a complete solution for education on reservations. “Additionally many tribes face 50 -80% unemployment and all the problems associated with poverty: single parent homes, poor nutrition, alcoholism, drug abuse, you name it, ” says Campbell. “It is hard for a kid who is surrounded by drugs and alcohol, who may not have eaten much in the last 24 hours to put a great deal of thought or effort into his/her studies. That is not to say that some great teachers have not inspired some great, motivated kids, but that is sadly the exception, not the rule.”

Other Tribal Issues

Maintaining tribal sovereignty is high on Campbell’s priority list. According to him, “The very survival of tribes as governments is at stake when sovereignty is under attack.” Campbell is working to pass the Inouye Amendment to the Employee Free Choice Act to treat tribes as governments.

He says he is also concerned about organized labor getting involved in tribal governance. “If labor injected itself into tribal politics,” says Campbell, “It would bring an outside dynamic, unfamiliar with tribal issues, into tribal politics and I believe that would be devastating to most tribes.”

Ben Nighthorse Campbell continues to be a strong advocate for Native American rights and says he is proud of recent progress. He concludes with cautious optimism, “Things are looking up but, we have very far to go.”

Cover of The Moore Method

Robert Lee Moore was a mathematician and teacher who spent the majority of his long career at the University of Texas at Austin. As a mathematician he is best known for his work in linear point set topology. As an instructor of mathematics he is known for a method of teaching that often bears his name (The Moore Method) or is sometimes called the “Texas Method” since several of his colleagues at the University of Texas were converts to and proponents of his way of teaching.

Published by the Mathematical Association of America as MAA Notes #75, The Moore Method brings together four expert researchers and university-level teachers of mathematics to describe their experiences and offer practical advice on how to implement this particular style of learner-centered instruction.

What is the Moore Method?

The Moore Method is a form of inquiry-based learning in which students are given minimal guidance and instruction and then must extend what they have been given to discover and prove new (to them) theorems in mathematics. Moore developed his ideas on how best to teach mathematics while at the University of Pennsylvania and used the method throughout his career at Texas from 1920 until his forced retirement (!) in 1969.

In Moore’s own version, he would provide a few clearly stated theorems and then assign students to solve problems (proofs generally) by only using what had been given, without collaboration or the use of any textbooks or outside materials of any kind. During class periods, students got credit by going to the board and presenting their work to the class as a whole at which time the class would discuss the problems, although students were not allowed to suggest improvements to another student’s work. Students got credit for being first to present the correct solution to a problem, after which, no one else could get credit for it.

A “How-to” Manual for the Moore Method

The “pure” Moore Method (minimal information, no lecture, no collaboration, no consulting of textbooks) seems rather harsh to many people. The criticism that it fosters too much competition, induces a “kill or be killed” classroom atmosphere, and favors strong students over weaker ones, are valid. However, rarely do any of the authors implement such a pure Moore Method in their own classes. The basic principles of minimal guidance, rare lectures, personal struggle and discovery, and presentation at the board are the common themes that seem to define the Moore Method.

The authors go into some detail describing exactly what the Moore Method looks like in one of their classes, how they prepare for teaching such a class, and how they each modify and adjust the class depending on the student makeup. Details are provided on how to grade such a class, how develop and select a set of notes (but not a textbook!) to support such a class, and on what problems and opportunities to look out for along the way.

The book concludes with a chapter discussing research into the effectiveness of the method (contributed by a different group of authors) and a useful collection of “Frequently Asked Questions” about the Moore Method. The main authors also generously provide as examples some of their own syllabuses, course notes, handouts and exams from a variety of courses they have taught using the method.

Although the majority of math instruction at the college level still is presented in lecture format (somewhere around 75%), a small but growing number of professors are moving in the direction of a more constructivist approach. This is one area where higher education is clearly trailing K-12 education, which has moved strongly toward learner-centered methods and mastery learning in recent years. With the work of the Legacy of R. L. Moore Project, more and more college professors are learning about and considering trying something “Moore style.”

The Mixed Legacy or R. L. Moore

Moore is not everyone’s favorite example of a fine mathematics teacher in action. He was a lifelong racist and refused to teach African American students. In this respect he was clearly out of touch with the changing times of the 60′s. Even so, he was far ahead of the curve with respect to developing and refining a method of instruction in which the student must take responsibility for his or her own learning and construct their own knowledge and understanding of a subject.

References

The Moore Method; Charles A. Coppin, W. Ted Mahavier, E. Lee May and G. Edgar Parker; Mathematical Association of America, Washington, DC: 2009

Dwight D. Jones

Note: I conducted this interview a couple years ago. Since the original site where it was published is slowly going down the tubes, I have transferred it to here to keep it available for historical reference. Mr. Jones is currently superintendent of a large school district in Nevada. Although he is no longer in charge of education in Colorado, it provides insight into his views on the challenges facing education not only in Colorado, but across the U.S.A.

Since taking the helm of the Colorado Department of Education, Dwight D. Jones has faced many challenges. He remains a staunch supporter of quality education in Colorado.

When the time came for Colorado’s State Board of Education to appoint a new commissioner of education in 2007, it was unanimous: Dwight D. Jones was their man. Jones was a teacher and administrator before becoming the superintendent of a district known for narrowing and eliminating achievement gaps related to minority children and students of low-socioeconomic means.
Closing the Achievement Gap

Jones has continued to focus on achievement at the state level. How much of a concern is the achievement gap in Colorado?

“I am concerned about the achievement gap that exists between students of various ethnic backgrounds, between students of families with different socio-economic means and, yes, between students from America and those of other industrialized countries,” says Commissioner Jones. “America has lost its competitive edge, particularly in the areas of science, technology, engineering and math (STEM), and this loss is to the detriment of both the students and our nation.”

Recognizing an achievement gap is one thing, but Jones says that Colorado is doing something about it. “In six districts—urban, suburban, rural, small, large, ethnically diverse—we are in the second year of a three-year pilot, in which targeted interventions and proven methods are being implemented in order to close the “race” and “income” gaps. One of the goals is to determine what works under what conditions and at what cost.”

Funding Education in Colorado

Other areas besides STEM-education are of concern. “The way education is funded poses many problems,” he says. “The “seat time vs. competency” debate continues about whether schools should receive per-pupil operating revenue (PPOR) based on student enrollment/attendance (seat time) or whether PPOR should be tied to student outcomes (competency). Teacher pay is a matter that needs to be addressed and remedied.”

How much of an influence do health care costs have on education funding in Colorado? According to Commissioner Jones, “Quite a bit.” He goes on to add, “Medicare program increases have by and large tapped out all other sources but education, and analysts believe education will be hit next. Ultimately this means fewer dollars will be allocated to education. Health insurance and related costs also affect education’s bottom line in districts. Districts that have self-funded insurance policies are greatly impacted. Individual claims against the insurance pool equate to higher premiums, as does the escalating cost of health care services in general.”
Preparing Students With 21st Century Learning

Like many other states, Colorado teachers strive to incorporate so-called 21st Century Skills into the classroom experience. Although not everyone agrees that 21st Century Skills should be a part of the curriculum, the commissioner is a strong supporter.

“Students have always needed to have critical thinking and decision-making skills. However, I believe these skills [21st Century] are even more important for today’s students because of the world in which we live. The advent of the Internet, the instantaneous nature of the media and a multitude of technological tools allow for the continual availability and distribution of information of all kinds.”

Jones says, “I believe it is vital that students be taught to evaluate both the nature of the information and the reliability of its source, to decipher fact from fiction. Only then will they truly expand their breadth and depth of knowledge and have a basis on which to for their own opinions.”

Improving Education in Colorado

When it comes to the biggest needs of students, Jones comes back to the achievement gap. “I am a firm believer that all children—whether they live in a big house or a small apartment, in a city, a suburb or on a farm many miles from the next town—can learn, achieve and excel, and deserve every opportunity to do so,” he says. “Accomplishing that will be a great improvement to education in Colorado.”

Despite ongoing challenges in funding and achievement, Colorado has done well in some areas. Jones points to the evolution and improvement of Colorado’s standards as a high point. “From their inception, Colorado’s model content standards—what we believe students should know and be able to do—have been noteworthy,” says Jones. He believes that ambitious standards are a critical component of a high-quality education.

According to Commissioner Jones, “The refinement and revision of the standards will make them more meaningful to both students and teachers. The governor’s Colorado Achievement Plan for Kids and other legislation passed by the Colorado General Assembly in recent years are putting things in place to ensure that all students receive a high quality education.”