## Saturday, December 17, 2016

### PRIMUS Issue on Teaching Inquiry and JMM Events

Hello IBL Community!  Brian Katz, Augustana College, has shares exiting news for IBL community. Please read below for special issues of PRIMUS and IBL-related events at JMM 2017 in Atlanta, GA.

PRIMUS special issue on Teaching Inquiry
Elizabeth Thoren and Brian Katz have organized the 19 papers and 2 editorials in this two-volume special issue around the ways that they contribute to the discussion of two questions: what is inquiry, and how do we support its development in students?

Part I, entitled Illuminating Inquiry,” focuses on the nature of inquiry, from discussions of its theoretical foundations and generalizations across disciplines to descriptions and analyses of the experience of inquiry from the inside. Part II, entitled “Implementing Inquiry,” focuses on approaches to offering inquiry experiences, from discussions of strategies to change student and instructor behaviors to descriptions and analyses of course design and project structures. Of course, a reader will find insight into both the nature of inquiry and approaches to achieving it in any paper in either part, and each part contains ideas for both instructors who have experience teaching with inquiry and those who are hoping to start. Each issue starts with an editorial that offers a more detailed overview and integration of the papers.

Illuminating Inquiry: http://www.tandfonline.com/toc/upri20/27/1?nav=tocList
Implementing Inquiry: http://www.tandfonline.com/toc/upri20/27/2?nav=tocList

1. PRIMUS special issue on Inquiry-Based Learning in First-year and Second-year Courses (forthcoming). Guest edited by Dana Ernst, TJ Hitchman, and Angie Hodge
2. MAA Instructional Practices Guide (forthcoming). This document is a companion to the MAA's Curriculum Guide that will focus on course design, instructional practices, and assessment. Doug Ensley and the project leadership are running focus groups related to this project at JMM 2017.

Joint Meetings of the American Mathematics Society and Mathematical Association of America, January 6-9, 2017, Atlanta, GA.

Here's a link to the full schedule: http://jointmathematicsmeetings.org/meetings/national/jmm2017/2180_progfull.html

The SIGMAA IBL is sponsoring a Contributed Paper Session with 55 talks on Inquiry-Based Teaching and Learning
• Thursday 1/5 8:00am-12noon (Regency Ballroom, Ballroom Level, Hyatt Regency). This session is specifically designed to be accessible and useful for new or potential IBL practitioners.
• Friday 1/6 8:00am-11:00am (International Room 6, International Level, Marriott Marquis). This session emphasizes lower-division and large course contexts.
• This session emphasizes lower-division and large course contexts. Friday 1/6 1:00pm-5:00pm (International Room 6, International Level, Marriott Marquis).   This session first emphasizes secondary school contexts and then turns to equity in mathematics education. NOTE that this session flows immediately into the SIGMAA IBL Business Meeting.
• Saturday 1/7 8:00am-12noon (International Room 7, International Level, Marriott Marquis).  This session emphasizes applied math and technology in inquiry.
• Saturday 1/7 1:00pm-4:20pm (International Room 7, International Level, Marriott Marquis.  This session mostly emphasizes the Calculus context.
SIGMAA IBL is also sponsoring a panel featuring Susan Crook, TJ Hitchman, and Carol Schumacher Thursday 1/5 1:00pm-2:20pm (International Room 5, International Level, Marriott Marquis)

SIGMAA IBL Business Meeting (interactive discussion) Friday 1/6 5:00pm-6:00pm (International Room 6, International Level, Marriott Marquis)

There are many other presentations about IBL at the conference, and conference attendees are especially suggest you browse the RUME and SoTL sessions.

## Friday, October 28, 2016

### A Vision for the Future of Active Learning: Professional Development Centers

I've been participating in the Mathematical Association of America's Active Learning Day/Week (#activelearningday), I've shared some videos of students sharing their opinions and experiences in IBL classes. I've also truly enjoyed hearing from my colleagues about their experiences and what they do! What an inspiration!

I think it's appropriate at this point to share an idea I have been thinking about for several years. The idea is centered on the goal of really pushing active learning forward in Mathematics. The idea is fairly straightforward, and is to create several Professional Development Centers in Mathematics Teaching and Learning across the nation, loosely modeled after the Mathematical Science Research Institute. Because regional needs vary significantly, it is likely a better strategy to create more of these in smaller sizes, creating a more nimble and responsive network.

Some Issues and Gaps
Some gaps in our system exist for preparing college math faculty to teach using active-learning methods exists. I'll highlight some of the main ones I have noticed to shed some light on the gaps, and then we can see how a PD Center can offer significant help.

Education reform is hard, time-consuming work. It involves working with people in diverse settings and in the system is gigantic. Just in my state university system, the California State University, there are 440,000 students across more than 20 campuses living in learning in a vast range of environments. Impactful change in just one system is an immense challenge, much less the challenge presented by a nation with over 300 million people.

Teaching is a system and a cultural activity. Hence change is much, much more than merely changing textbooks or rearranging the schedule from MW to MWF. It involves shifting fundamental ways in which students interact with the subject, which involves a lot of inertia. Hence, this is yet another factor that implies that changes in teaching is a hard challenge for each individual instructor.

The Uptake Problem is a label I use to represent the fact that the percentage of faculty using active-learning remains low, despite knowledge of the existence of active learning. One study by Dancy and Henderson suggests that time and other complexities affecting the process of changing teaching methods are significant. It's not enough to know a solution exists. To find ones that work for individuals is a specialized problem confronting each instructor.

Grant work has been instrumental in accelerating the progress of active learning, and we have gained and learned a tremendous amount from this. We would not be where we are today, without grant-funded projects. The grant-funded projects, however, do not cover all the bases, so arguing that we have external grants isn't a full solution. For instance, when funding ends, projects can lose momentum or die off. We can say that we are at a point where we can see the finish line because of grant-funded work. We are much better off, but this line of work tends to be more focused and not the broad, long-term work we need to take things to the next level.

At present, there isn't a professional group that works solely on implementation of active learning on a full-time basis. This is in my opinion a weakness in the system, and slows progress. Grants allow some of us to do this part-time, but our time frames are short and our reach is limited compared to the size of the profession. At the moment, we are primarily a grass-roots effort (which is good and necessary, but not sufficient).

Centers for Teaching and Learning on college and university campuses are wonderful resources. I truly appreciate what they do and the services they offer. One area that CTLs can struggle with is in the area of the details of discipline specific active learning. Teaching Abstract Algebra or Real Analysis or first-year Calculus present different challenges to math instructors. Hence, mathematicians and mathematics educators are best positioned to be the ones to do the PD work. General frameworks for teaching are a good place to start, and can be learned from CTLs, but what happens when your students have trouble understanding nested quantifiers in the context of proving a function is not continuous? CTLs can be partners in this, but another force is needed to take things across the finish line.

Experienced faculty in active learning are generally diffuse and are (at least) somewhat isolated from one another. At the moment there are some efforts to coordinate, so it is understood by some that this issue needs to be addressed. Still much of the time the experience, skill, and knowledge of the profession is not being fully harnessed via collaboration, sharing, and consolidating knowledge, materials, and expertise. Consequently, a PD Center is needed to assist with coordinating efforts.

Hence, opportunities to learn about and get support using active learning are largely ephemeral, and all the while the challenges facing instructions remain significant.

What Professional Development Centers Could Do
I'll sketch the kinds of activities PD Centers could do. This isn't a comprehensive list, and is intended as a staring point to explore what might be possible.
• Focused on professional development for all faculty interested in active learning and improving student learning of mathematics
• Short workshops, during academic terms, where faculty could visit classes
• Long workshops during academic breaks for intensive work
• Traveling workshops to visit to departments
• Create repositories for workshop materials, course materials, and relevant research studies
• Postdoc and visiting scholar programs for developing young faculty and future leadership
• Host small groups of visitors during the academic year to customize experiences around their specific needs
• Create a video library of best practices for multiple types of classes, so visitors can sit in live classrooms and study video to ensure they have access to the range of skills and practices needed for successful implementation. The video library would also have value in formal workshop settings.
• Outreach work to encourage an ever increasing number of instructors to lean in and try active learning
• Develop workshop leaders so that workshops can be run across the nation.
• Offer grants to support faculty and departments, who need time and materials to get up to speed
• Full time faculty and staff, who focus on this line of work, perhaps including postdocs and visiting scholars
My sense is that a PD Center should be housed at a college or university, where teaching is valued and a variety of course offerings are available. In this case, it could offer many different options for professional development.

Our experiences running IBL Workshops inform us that changes in teaching requires significant time and effort. The typical new IBL instructor spends hundreds of hours to get going with IBL, even when starting with a week-long workshop.  The "activation energy" is high, and efforts are spent over many academic years. A PD Center could offer support that matches such longer-term time frames for faculty development and institutional changes, unlike grant-funded projects, which come and go and have more limited resources.

Let's look at the example of the state of California, which has about 1/8th of the nation's population. I'm choosing this example only because this is where I am. A PD center somewhere on one of the CSU or UC campuses, could be a place where math professors and instructors from colleges and universities across the state (and west coast) could visit within a half a day's drive or short flight. Annual workshops and conferences could be hosted, and specific regional issues could be addressed, such as the preparation of future secondary math teachers, how to teach Differential Equations to engineering majors, urban commuter issues in the SF and LA areas, and so on... Steady, long-term effort could be spent on a wide range of issues with the help and support of a PD Center that brings people together to work collaboratively on our big challenges.

Consequently, it can be argued that the existence of PD Centers would significantly impact the long-term successful implementation of active learning across the nation. These efforts could be expanded into other STEM fields, and in time (or in parallel) into K-12 Math and Science.  We have a robust group of mathematicians, mathematics education researchers, and math instructors across the nation, all doing great work. The ideas outlined above expose where our nation is lacking in infrastructure, and how some of these gaps could be addressed with PD Centers.

Great schools depend on great teachers. Focusing our efforts on teaching and learning is, in my opinion, the best bang for the buck. It would be wonderful if we could provide the support, leadership, and vision befitting the challenges, needs, and goals of our math teachers, our profession, and ultimately our students.

## Monday, October 17, 2016

### Does Class Size Matter?

Let's look at some data. An analysis released a couple of years ago by the National Education Policy Center uses an econometric take on the issue, where they try to disentangle data to find causal links. In their work, share evidence that class size increases harms students. This is from data that is "econometric" friendly, where the savings today in increasing class sizes (K-12) is offset in the future by far greater costs. (Penny wise, pound foolish?)

The point I want to get to is a very simple one. Another perspective of this issue is as a classroom teacher.  Let's look at the sequence of class sizes to see how teaching decisions are affected as class size increases. (The assumptions here include assuming we are talking about the college math setting.) Also I'm not going to list all possibilities. The goal here is to see a pattern as class size increases.

Class size of 10: Anything can be done at this class size. Projects, full IBL (where students present proofs or solutions), team/group work, seminar or whatever comes to mind.

Class size of 20: At 20, things are still manageable, and an instructor can get to know all of the students, customize materials and learning experiences, projects are still doable. IBL is doable in with small groups/pairs and students presenting individually.

Class size of 40: Things start to get to a point where there are too many students to let them present their work to the whole class.  Each student may only go to the board a couple of times a term. Somewhere between 30 and 40, instructors tend to switch away from some student-centered methods (such as students presenting their ideas at the board). Small groups can still be used, and the instructor may not be able to get to all groups on a particular task.

Class size of 80: Individual student presentation of mathematics is almost surely off the table. Small groups and peer instruction remain, so instructors can develop this area to support an active learning environment. Projects are highly difficult to implement at this class size, especially at institutions without teaching assistants. The instructor can still visit with some groups and make it around the room (depending on the space) say one trip per class period (approximately).

Class size of 160: At this point, you are well into large lecture territory.  Peer instruction (Think-Pair-Share) and similar methods (with or without clickers) remain in play, although the size or difficulty of the task may be on the less challenging side of the spectrum. Presentations by students, class discussions, projects, instructor visits to each group regularly are almost surely off the table.

As you go up in class size, you lose the implementability of teaching strategies that engage students and also anything that does get implemented needs to be done at a higher skill level and attendant time in preparing for class. Managing a discussion with 160 students takes skill, and most all instructors may be inclined to avoid it.

Consequently, what we are seeing is that there exists research evidence suggesting that a negative, material impact is a consequence of increasing class size AND from a practitioner standpoint instructors have fewer, high-impact strategies at their disposal as classes get larger. We have said nothing yet about how class dynamics can change as you get to larger class sizes. For example, it's easier to hide in a large class, and it's easier for students to checkout, be distracted, and show up late.

Another facet of class size issues is that class size is often a policy decision, not in direct control by an instructor. Instructors can have input on class size, but it's not up to instructors to set class size limits. This is done by policy makers or administrators, yet these decisions have significant impact on teaching decisions and hence learning outcomes. Faculty and administrators should take into account the big picture when it comes to class size. Focus on things like nominal efficiency, should be viewed while also heavily weighing learning outcomes, DFW rates and long-term impacts on student learning.

## Thursday, September 1, 2016

### Effort and Circumstances in Educational Achievement

The educational achievement by a student is not only a result of personal effort, but is also dependent on circumstances. Student accomplishments are not acts by a single person, but are also deeply influenced by the circumstances (or environment) in which they live and learn. A factor that often doesn't get the attention it deservers are the circumstances of students as a critical component in student success. This is a multilayered topic, and the goal of this post is to shed some light on the issues.

Before we dive into the details, an obvious sign of the importance of circumstances is the stress parents feel when figuring out what schools to send their children. It's a clear signal that where kids go to school and the people at the school matter. Yet strangely and in near complete contradiction, the notion that education is a solely individual accomplishment exists.

Math Analogy:  There's a difference between functions of one variable and functions of two or more variables.  Symbolically let $x$ be student effort, and let $y$ represent a student's circumstances. Then what is being asserted is that $f$, a student's achievement (whatever that means), is dependent on $x$ and $y$. As math teachers, we may be prone to looking at teaching as $f(x)$ and not $f(x,y)$ perhaps tacitly or perhaps because we don't know what more can be done.

What does $y$ represent? There are of course the usual things. These are factors like location, family income, ethnicity, poverty, school quality, parents' level of education, and so on.  Additionally we can include schools within the broad category of circumstances. Class environment, curricula, daily schedules, the architecture of the buildings, the number of students in the classes, the teachers, ... all these in the aggregate make up $y$.

Claim: $f(x,y)$ is highly sensitive on $y$.

Rationale:  There's evidence that suggests the sensitivity of $f$ on $y$ is rather significant. In a recent article by Ellis, Fosdick, Rasmussen, evidence is presented suggesting calculus apprehensions can steer women out of the STEM pipeline at 1.5 time the rate compared to men. Simultaneously we also know that the use of IBL reduces sizable gender gaps between men and women compared to non-IBL, traditionally taught courses. (See Laursen, Hassi, Kogan and Weston.)  That is, even changing $y$ by only factors limited to classroom pedagogy can change $f$ in ways we can measure statistically.

Researchers in Germany dig partially into circumstances under the label "Error Climate" (Link to a description 1, Link to description 2).  Steuer and Dresel identify factors that support a positive learning environment, such as empowering students to be willing to experiment and try.  In their work they identify factors that are related to how teachers teach and pedagogy.

1.  Error tolerance by the teacher
2.  Irrelevance of errors for assessment
3.  Teacher support following errors
4.  Absence of negative teacher reactions
5.  Absence of negative classmate reactions
6.  Taking the error risk
7.  Analysis of errors
8.  Functionality of errors for learning

In active, student-centered classes these items can be integrated. Mistakes can be de-stigmatized, and students can learn growth mindsets. We can't do much of anything about factors like poverty, at least not directly via classroom instruction. We can, however, do something about our classroom environments that can minimize gender gaps and other inequities.  Small group work, student presentations, portfolios, projects, productive failure are just a handful of IBL strategies that can be used to create a significantly different set of circumstances for your students.

Additive improvement:  Improving teaching often is focused on $x$, or student effort, via things like books, ordering of topics, clearer exposition, better problem sets, getting students to do homework. These are aimed at the experiences of the student and their effort on the subject. Those are of course good places to expend energy, and what I am suggesting is to add.  Add consideration and teacher effort on $y$, without diminished hard won successes in $x$. That is, improving $f$ optimally includes working on $x$ and $y$, and this is not a zero sum game. Instructors do not have to give up proportionally one to gain in the other.

Francis Su eloquently makes the case in his talk, Freedom Through Inquiry. He shares the story of Gloria Watkins, who experienced two starkly different realities in her education during the change from segregated schools to bussing and integration. Su, an MAA President and accomplished mathematician, shares his personal story about perseverance. The environment in which he grows up in and his educational experiences have made a material impact on his career trajectory and life.
"And just like Watkins, I had professors who didn’t believe I was capable of making it through, especially when I failed my qualifying exams the first time...
It’s because I had that inquiry-based Moore-method class with Starbird that I knew that I could do research. I already had the experience of discovering things for myself. I knew that I knew how to ask good questions, because we had the freedom to ask any question in Starbird’s class and figure out which ones were fruitful. And I knew how to use those questions as a springboard to independent investigation.
And because of that, I knew, no matter what anyone said or believed about me, that I could push through. Today’s literature suggests that inquiry-based teaching methods confer significant benefits on underprepared students, and of course I believe it. Because I’ve lived it."
Teachers have opportunities to make transformative changes. Expanding our view to see more variables related to learning helps us see more opportunities to help students succeed. While there are limits, constraints, and societal-level issues that form daunting challenges to improving the circumstances surrounding our students, nevertheless there still exists real and significant opportunities for change, right here in front of us in our classes!

Ellis, Fosdick, Rasmussen
Error Tolerance
Freedom Through Inquiry by Francis Su

## Thursday, August 25, 2016

### Students Voices: Taylor

Taylor is a Liberal Studies major (Elementary Education) at Cal Poly, and shares her thoughts about her IBL experiences in Professor Grundmeier's IBL Math for Elementary Teaching classes.

Transformative experiences come in different forms.  In this case, Taylor learned about herself. She learned that she is a math teacher and her experiences in IBL math classes showed her a pathway towards a career in secondary math teaching!

"There's not just one way to solve a math problem..."

## Wednesday, August 24, 2016

### Beginning of Fall: IBL Blog Playlist

I want to wish all teachers starting their terms now or in a few weeks the very best. The start of a school year is a busy time, and much thought and effort goes into getting up to speed with classes, advising, mentoring, committee work, and on and on. Upward and onward!

We recently compiled an IBL Blog Playlist. This playlist has some of the main ideas we have shared over the years, compiled on a single page. Blog posts were reactions to needs discovered in our work in the IBL community, and over time it has become hard to find the older posts that are still relevant.  We'll keep updating the playlist periodically to keep up with content.

Quick point: If you can do only one thing IBLish, try Think-Pair-Share!

## Wednesday, August 17, 2016

### CBMS Statement on Active Learning

Okay, this is a really big deal.  The Conference Board of the Mathematical Sciences has weighed in. CBMS supports active learning (CBMS Active Learning Statement)!

Just to be clear, this isn't one or two professors clicking a like button on social media. Let's take a look at the CBMS member societies:

• AMATYC, American Mathematical Association of Two-Year Colleges
• AMS, American Mathematical Society
• AMTE, Association of Mathematics Teacher Educators
• ASA, American Statistical Association
• ASL, Association for Symbolic Logic
• AWM, Association for Women in Mathematics
• ASSM, Association of State Supervisors of Mathematics
• BBA, Benjamin Banneker Association
• IMS, Institute of Mathematical Statistics
• INFORMS, Institute for Operations Research and the Management Sciences
• MAA, Mathematical Association of America
• NAM, National Association of Mathematicians
• NCSM, National Council of Supervisors of Mathematics
• NCTM, National Council of Teachers of Mathematics
• SIAM, Society for Industrial and Applied Mathematics
• SOA, Society of Actuaries
• TODOS, TODOS: Mathematics for ALL

These are the main players in college-level mathematics (and PreK-12 mathematics).  They have all signed on to supporting active learning, because "A wealth of research has provided clear evidence that active
learning results in better student performance and retention than more traditional, passive forms of instruction alone. "

The statement goes on to say in bold, "...we call on institutions of higher education, mathematics departments and the mathematics faculty, public policy-makers, and funding agencies to invest time and resources to ensure that effective active learning is incorporated into post-secondary mathematics classrooms."

It needs to be stressed, that active learning and IBL are not fads or fashion statements. These are methods that have been developed over long time periods. Certainly it takes much more work and energy to successfully teach via active learning (e.g. IBL), and for people like me it's not worth it, if it doesn't work.  I have better things to do with my time than just do things for stylistic reasons in my classes.  But we have a lot more evidence now that students learn better, retain more, and inequities like gender bias can be mitigated via active learning strategies.

If you have not done so yet, I encourage you to take a step towards actively engaging your students!

## Thursday, June 2, 2016

### 10+ Videos on Productive Failure (Playlist)

Productive failure is increasingly becoming an important aspect in teaching, in light of the growth mindset research that have been published recently.  Below is a short list of videos I find useful to share with students.

1. Michael Jordan "Failure" Commercial

2. Sal Khan interviews Carol Dweck on Growth Mindset

3. John Legend, Musician: "Success through Effort"

4. IBL Instructors discuss the importance of failure

5. Growth Mindset Animation

6. Mike Starbird: Study Skills and Making Mistakes

7. Study Skills: Learning From Mistakes (Jo Boaler)

8. Diana Laufenberg: How to Learn from Mistakes

9. Uri Alon: Why Truly Innovative Science Demands a Leap into the Unknown

10. Astro Teller: The Unexpected Benefit of Celebrating Failure

Edit:

11. One more suggested by Bret Benesh: Ira Glass

12. Thanks to Jane Cushman for sending me this:  Karen Schultz, On Being Wrong

## Thursday, May 26, 2016

### For Parents of K-12 Students (U.S.)

Dear Parents,
Every weekday morning I drop off my son at school.  Every weekday afternoon I pick him up. I have a vested interest in the success of schools both personally and professionally. When I talk to parents about their children’s education, I have noticed, however, that most parents have major gaps in their understanding of how our education system works, Common Core, active learning, and the point of education. In this post, I hope to nudge you to learn more about the issue for the sake of our children.

Before we can talk about the main issues, we need to be clear on the basics. Some parents I talk to do not understand the “ingredients" of education. Just like cooking, you need to get the right ingredients, and on an even more basic level be able to recognize what those ingredients are.

Basic ingredients of Education (in the US):
• The state standards
•  Curriculum (books and textbooks)
• Teaching (Instruction) and learning environment
• Student Learning
• Assessment
• Other (e.g. counseling, sports, clubs, facilities, etc.)

Looking at a list of ingredients doesn’t convey what the final product is. If you get recipe and only look at the list of ingredients, it doesn't tell you what the final dish will be when served.  Education (as a system) is much more complex than cooking a meal.  Hence, we need a way to organize the information to help us make sense of what we perceive at our schools.

Models let us see better how the pieces fit together, by organizing them in a structure.  The simple model below shows more or less how the basic ingredients fit together. It's not meant to be a definitive model covering all aspects of education. We're going to use the model to illustrate key points.
Your state (not the federal government) sets the standards. School standards then eventually result in textbooks that cover the standards. From there, teachers must take these pieces (and other resources) and incorporate them into their teaching system, and design classroom activities. Teachers must also customize the learning experiences to the actual students they have in the classroom. Student experiences and mindsets vary significantly, and day-to-day instruction adapts according to student learning needs.

An Example of How Some Parents Can Blame the Wrong Thing
I hear a ton of Common Core bashing, and what I hear is a lack of understanding of what education is, what standards are, and what standards are not. I noticed a particular example of this recently. Let's first set this up.

In grades K-6, research on homework strongly suggests that there's no learning gains for homework. It does perhaps cause students to dislike subjects or learning in some cases, so in sum it's a bad idea. High performing nations like Finland essentially do away with homework.

So homework in K-6 doesn't do anything for some students, and for others it's a net negative. The policy that should be adopted is to eliminate homework or reduce it significantly in elementary grades. Despite this research, parent often ask for homework, because that is what they grew up with.

Where things go wrong is when a teacher (in the US) is implementing math, such as in Common Core, where in addition to learning skills, students are also asked to think, explain, experiment, problem solve. This type of curriculum needs a carefully designed class experience and parents who understand that doing math well means doing math like mathematicians. That is, making mistakes, experimenting, and taking time to think deeply about the concepts. This is math that is far beyond what most parents experienced. In contrast, in order to placate parents who want the usual homework assignments, teachers send students home with math homework that often has good problems, but these are problems that take longer and require thought. Getting stuck is likely.  So here we have (a) teaching methodology that isn't going to work, based on research evidence, and (b) homework that is challenging that parents, who may have math anxiety will get into a homework-frustration struggle with their kids (at the end of the day, with dinner to cook...) This is a classic "conflating implementation struggles in the early years" with "the standards are a bad idea."

An added layer is that most people think doing math faster means smarter, and doing math slower means dumber. Misconceptions about Math and the nature of learning feed anxieties further, and then the blame game starts. Something has to be wrong, if Johnny can't add!

The final act of this tragedy is that people then assign blame to the wrong thing. They blame the standards, not the environment of parental pressure and the asking for homework in elementary grades. The standards aren't the problem here. It's instruction and how our society doesn't fully let teachers do their job and apply evidence-based practices. If anything, we (parents) make it harder for teachers to switch to better teaching methods.
If the goal is to improve education, then it's important to focus attention and effort on the correct thing. Helping and supporting teachers implement their curriculum as they were intended is what should be the focus. Instead, people want to tear down the standards (which will not improve education), and likely see us return to methods and curricula that have been shown to be significantly flawed and problematic.

Conflating Assessment and Standards
Here's another example. One of the other large pressures putting teachers and staff in a tough place is assessment. In the U.S. we assess too much, and those assessments use huge resources, and are then tied to job security. This creates unintended, "perverse" incentives that make schools teach toward narrow tests, at the expense of a fuller, holistic education. The arts, music, dance, etc. get nixed, only making it harder for children to find their element. Their passions.

Assessment should be done in scientifically sound ways to see how our schools are doing. The reality is that testing is far too large a force, and actually dominates education choices. Parents sometimes see this. They see too much assessment as a problem, where test results are used to punish or threaten teachers or administrators.  Instead of pushing back at the testing regime (and the massive testing industry behind it), some parents blame the state standards.
The issue here is quite clear again. The wrong ingredient has been identified as the problem. When you go in for knee surgery, you want to make sure the surgeon works on the correct one. Well, this is the same sort of thing. The torn ACL is on the left, but we've done surgery on the right. Most people would agree that it taking a step back, and not solving the real problem.

Understand the Problem First
What can parents do? One of the ideas we try to teach students at all levels it to understand what the problem is saying first, before making conclusions. We want students to ask pertinent questions, and understand the components of the question and the context surrounding it.  I think this lesson applies broadly. Parents in particular can learn more about education and what the actual issues are, BEFORE forming an opinion. Otherwise, you're committing a basic intellectual mistake or sin, called intellectual indulgence. (Intellectual indulgence is when you believe something to be true, because you like how it sounds, and not because you have any good evidence to support it.)

Ignorance is not a virtue, especially when it comes to decisions and policies about education. In fact, ignorance is damaging. Our society's collective, group ignorance prevents us from achieving far more than what we have. People have strong opinions about education and can prescribe or criticize, even when they do not have even a very basic understanding of what education is, how it's constructed, and what it's for. I hope you can see the deep and tragic irony with ignorance about education.

Parents can start with the books and videos listed below to learn more about growth mindset, what math education is like currently, how it could improve in the US, and how international comparisons shed light on what we can do better. Parents obviously matter a great deal, and an informed group of parents with a positive, constructive attitude can be a powerful force in supporting and shaping our education system.

I have seen it time and again. When teachers are supported by their community and get it right, I see students transform from passive, disengaged people to eager, vibrant learners. Parents come up to me and say things like, "My daughter likes math this year!" There is good reason to be optimistic today, as we have learned much about how to effectively teach. The problem and challenge of improving education is a tractable problem. Parents can choose today to be a positive contributor to this process. You can say to your kids, "Hey, I'm going to show you how I learn about something by doing my own research..." And what a wonderful thing that would be to teach your children!

References for Parents
1. Mindset, by Carol Dweck
2. What's Math Got to Do With It, Boaler
3. Mathematical Mindsets, Boaler
4. The Teaching Gap, Hiebert and Stigler

1. Carol Dweck on Mindset

2. Jo Boaler on Common Core

4. Dan Meyer on Teaching Mathematics

5. Ken Robinson on Education

## Thursday, May 19, 2016

### New AIBL Website

A quick post to say the AIBL Website has been updated with a new look! Check out www.inquirybasedlearning.org

## Monday, April 25, 2016

### A Practical Solution to "What We Say/What They Hear"

“In art intentions are not sufficient and, as we say in Spanish, love must be proved by deeds and not by reasons. What one does is what counts and not what one had the intention of doing.”  -- Pablo Picasso

It's my belief that teachers at all levels have good intentions and genuinely want their students to learn.  What this post is about is the notion that instructor intentions are not sufficient, and getting students to do what is needed for authentic learning is what counts.

Background
The starting point is for the ideas I want to get across from a the Launchings Blog of the MAA.  David Bressoud does a wonderful job of describing a recent paper by Kristen Lew, Tim Fukawa-Connelly, Juan Pablo Mejia-Ramos, and Keith Weber.

Below are links to Bressoud's twin posts.  They are worth the time!
"What We Say/What They Hear I"
"What We Say/What They Hear II"

The short version is presented in this diagram

Despite multiple passes through the proof and explanations, students in the study have a difficult time pulling out the instructor's intended messages in the proof and the instructor's spoken comments.  At first glance this makes sense, as the "information transfer" model doesn't work so well when the goal is "developing critical thinking."

As mentioned by Bressoud, Annie and John Selden and others have documented the difficulties students have with analyzing, proving, generalizing, packing/unpacking statements, etc. Learning higher mathematics is challenging, and most math majors struggle with learning proof.

Bressoud suggests options like flipped classrooms and clickers can work, but he notes that such methods have high initial investment in time and requisite knowledge and skill.  While these methods are learnable, many instructors may be in situations, where implementing them is not practicably feasible.  Other options are needed.

Another Option Exists!
Now to the main point of this post. There exists an "easy entry, high upside" method to help students come away with the intended messages.  Put simply, instructors can take their list of intended messages and turn them into math tasks. These tasks can be deployed via small group work, homework, etc.

Let's take a closer look. The intended messages of the instructor in the study are
1. Cauchy sequences can be thought of as sequences that “bunch up”
2. One can prove a sequence with an unknown limit converges by showing it is Cauchy
3. This proof shows how one sets up a proof that a sequence is Cauchy
4. The triangle inequality is useful in proving series in absolute value formulae are small
5. The geometric series formula is part of the mathematical toolbox that can be used to keep some desired quantities small
Each of these five points can be turned into "after the proof" problems.  They can be reformulated as
1. Explain using sentences and diagrams why Cauchy sequences "bunch up."
2. True or False and Explain:  One can prove a sequence with an unknown limit converges by showing it is Cauchy.
3. In the proof, find the part that proves the sequence is Cauchy.
4. In the proof, find the part where the triangle inequality is used, and then identify a general strategy based on this specific instance that you can put in your mathematical toolbox.
5. Explain how the geometric series is part of a mathematical toolbox to keep some desired quantities small.
One way to deploy these in the classroom is to present the proof on the board or pass out a handout with the proof, and then have students work through some of the tasks in pairs and then share (i.e. Think-Pair-Share).  If time is an issue, doing one or two and assign the rest for homework.  Alternatively instructors could ask students to read the proof before class, and the instructor could highlight the proof and spend more time on student-centered tasks in class.

Several advantages exist with this option compared to flipped classes or using clickers.  The first advantage is that it requires the least experience and least amount of pre-class planning or classroom equipment.  One could be in classrooms like I sometimes teach in with no technology, old boards, and desks built 50 years ago.

Another advantage is that it does not require deep knowledge of common misconceptions.  Instead, the instructor asks students to explain their thinking (in one way or another) and that's how the instructor gets insights into student thinking.  That is, use an activity and gather formative assessment.

A third advantage of this method is that it does not deviate from the conventional class prep process used by most instructors. Preparing presentations of a proof with explanations is something that instructors have done many times. The method presented here tweaks the process by transforming the intended messages that instructors would normally say to students into concrete mathematical tasks for students to work on. This change is practically feasible and doesn't require a significant alteration of an instructor's workflow.  It's also a step towards active, student-centered teaching and can be built upon over time into forms of teaching that more deeply engages students, such as IBL.

Instructors have good intentions and intended messages. I claim that it is how the intended messages are deployed in class that can be addressed in practical and effective ways. We can turn those amazing insights into amazing learning experiences, and "let problems do the talking!"

## Friday, April 15, 2016

### IBL Workshop Model and Real-World Results (Wonkish)

This post is about professional development, and is intended for those interested in faculty professional development.  There may be some applicability to K-12 PD, but I'm not promising that. Presented here is a model that I argue can be used outside of Mathematics in higher ed. My experience in K-12 PD tells me that changes can be made for K-12, but that there are other aspects (such as working with school districts, parents, testing, etc.) that add more layers that need to be carefully and thoughtfully handled (that may require much more resources).

This post is also from the perspective of people on the front lines. Our team works with teachers, and we are teachers.  Our work is grounded in the hard efforts of teachers who have thought carefully about the issues.

The evaluators for the project I've been working on are Dr. Sandra Laursen and Chuck Hayward, at Ethnography and Evaluation Research, CU Boulder.   We have run a set of IBL workshops (funded by NSF SPIGOT) in 2013-2015, and have some results to share.

The main results:
• Total number of participants is 138
• ~ 75% implementation rate
• 61% of the participants are in the first 5 years of their teaching careers.
• In just the first year after the workshop, participants taught 180+ classes to 4600+ students (in the real world)!
• Ongoing support via Email mentoring is a critical feature
• An inclusive or "Big Tent" definition of IBL is critical for allowing participants to find their own way, suitable for their situation.
The short version is that uptake is happening at a high rate!  This is an encouraging sign, as it provides evidence that effective PD can make a difference.

How we got to these results is a very, very large undertaking spread over about a decade of work by a team of people.  I'll briefly highlight the main facets in the rest of this post.  An embedded slideshow appears farther down this post with more details and diagrams.

First, we identified major obstacles that faculty face when learning to implement IBL methods.   If an instructor has not had much or any firsthand experience with IBL, it is hard to convey through discussions what an IBL class is like and how to pull it off. Additionally, there are skills, practices, curricula, and assessment to consider, all of which are different or changes.   Hence the need for a highly specialized professional development experience that directly addresses the challenges and needs new IBL instructors deal with.

Obstacles or challenges include lack of experience with IBL,  the need for instructors to learn IBL teaching skills, the Math Ed Knowledge Gap, IBL course materials, assessment in IBL courses, and organizing the structure (i.e. syllabus) of an IBL course. With a list of obstacles in hand, much effort went into designing workshop components to direct address and reduce the identified barriers.

It it emphasized that the workshop is designed as a single composition, where all the parts of the workshop are interconnected and the main goal is getting participants to a point where they can teach an IBL class successfully.  It is definitely NOT about trotting out our favorite activities.  Indeed, teaching is a system, and teaching is a cultural activity. Hence, the workshop is about providing a broad IBL framework that participants can adapt to their situation. The main focal points are (a) IBL teaching skills and practices, (b) understanding the evidence for IBL and how students learn, (c) linked teaching choices (assessment, problem posing, and content), and (d) building a practically feasible (to the participant) course.

Another important feature of our work is data driven decision making. The staff used evaluation data and research to inform decisions about all aspects of running and designing workshops, from recruitment, building workshops materials, adapting sessions to better meet participant needs, and also to main components that are successful.  It's through this iterative, self-assessment process that the workshop model has improved over time.  Sandra Laursen and Chuck Hayward head up the evaluation and research efforts for our projects, and their regular insights helps use make small and longer-term positive changes.

Our current NSF funded project, PRODUCT, has the main goal of expanding the profession's capacity to offer a version of the 4-Day IBL Workshop and developing short workshops that can be "sent" around the country and increase awareness of IBL.  The goal is to build the PD network up to a point where a much larger capacity PD exists and a larger variety of workshops (weeklong and short workshops).

More details are in the slides below.