My work with the AIMS team began last month after 20 years in public education, first as an elementary teacher and later as a mathematics coach. I have spent a lot of hours in TK-12 classrooms, walking alongside teachers as they explored ways to make their classrooms places where authentic mathematics learning could happen. In all of this work I have come to understand teaching and learning as innately human activities that connect us to one another through conversation.

Conversations happen in many settings. Think about the last time you gathered around the dinner table with friends. One person starts to tell a story. Another friend chimes in. Soon everyone starts nodding and laughing in agreement. Then one person tells a slightly different version of the story, revealing details from a different perspective. Discussion follows. Perhaps the story is revised further. More laughing follows. Then there’s the quiet lull that indicates collaborative satisfaction. The interpretation of a story is negotiated through contributions around the dinner table.

I’ve been deeply inspired by Paulo Freire, the notable Brazilian educator and philosopher. Freire was committed to dialogue that affirmed the human construction of meaning. “Dialogue is a way of knowing,” Freire wrote. “Dialogue cannot be reduced to the act of one person’s depositing ideas in another, nor can it become a simple exchange of ideas to be consumed… Because dialogue is an encounter among women and men who name the world, it must not be a situation where some name on behalf of others… Dialogue further requires an intense faith in humankind, faith in their power to make and remake, to create and re-create, faith in their vocation to be more fully human.”

At the AIMS center we have faith in children. We have faith in their innate, human ability to make and remake, to create and re-create. And we have faith in teachers and their ability to listen to children. Because of this faith, we’re committed to dialogue about how children come to know. Our Early Mathematics Team is particularly interested in how 3-5 year olds develop early counting and number concepts. Much of our work involves conversations with young children–not conversations in which we “deposit” ideas into children, but rather conversations through which we begin to think like children, to seek to understand their approaches, to explore what their mathematical knowledge might be like.

As we spend time in preschool classrooms and observe children interacting within their physical environments, it’s very clear that early learning involves dialogue. We know from our efforts to understand the ideas of Piaget and other constructivists that children learn from dialogue with others. In fact, it has been suggested in this work that interactions with others are among the most frequent causes of learning.

So, let’s engage in conversation. We’ll learn more about each other and ourselves as a result. It is, after all, a very human thing to do.


Further Reading

Freire, P. (1970). Pedagogy of the Oppressed. Myra Bergman Ramos, trans. New York, NY: Continuum.
Freire, P., & Macedo, D. (1995). A dialogue: Culture, language, and race. Harvard Educational Review, 65(3), 377-403.
Von Glasersfeld, E. (1995). Radical Constructivism: A Way of Knowing and Learning. Studies in Mathematics Education Series: 6. Bristol, PA: Falmer Press, Taylor & Francis Inc.

Less than a month after I read Ilana Horn's thoughtful post on teacher professional development, "Professional Development is Broken, But Be Careful How We Fix It," I came across this article from Education Week:

Here's a brief definition of micro-credentialing from the article:

​The article goes on to say that sometimes these badges are accompanied by salary increases worth several hundred dollars.

While this trend isn't likely to replace traditional professional development, it strikes me as an interesting response to the need for teachers to develop new and improved skills.

Fundamental to the idea of micro-credentialing is the belief that there are specific competencies that are crucial to teaching, and that these skills can be learned and measured. The folks at University of Michigan's TeachingWorks would agree. They've defined what they call high-leverage instructional practices and are working to create a National Observational Teaching Examination which uses on-demand performance assessments to measure teacher readiness. Researchers at Massey University, New Zealand, explain, "Routines capture the certainties within teaching, and as such can be anticipated and can become part of a knowledge base for learning how to teach."

Here's what I like about micro-credentialing for developing these routines:

​1. Jim Knight says, "Goals that others choose for us seldom motivate us to change." Micro-credentialing could allow for self-organized cohorts of teachers to select a teaching practice, connect with an instructional coach, explore the teaching practice together, interact with students, and collect evidence of their implementation. That's sound practice.

2. Micro-credentialing could place the burden of proof in the hands of the teacher: collect student work, create a video of your practice, utilize peer observation. In other words, you choose the evidence. 

3. Teachers who participate in this process are encouraged to implement, submit for approval, and then serve as reviewers for colleagues. This could generate a culture of adult-learning that could be contagious.

Inherent in any system that assigns rewards is the understanding that much of what goes on will be unrewarded. In my work with teachers, a consistent tension is present between developing proficiency in specific competencies and developing a general adaptability to students in the classroom. From Anthony and colleagues at Massey University: "Signifying adaptive expertise, they (teachers) pursue the knowledge of why and under which conditions certain approaches have to be used or new approaches have to be devised."
​

Teacher: I adapted to my students today. Do I get a badge now?
Reviewer: Sorry, there's no micro-credential for that.
​

Now on to some concerns about micro-credentialing:

1. External reward systems obscure and often negate internal rewards. Are external rewards necessary because we've done such a poor job of helping teachers recognize the indirect, sometimes hidden, rewards in the lives of their students? As Parker Palmer writes, "As important as methods may be, the most practical thing we can achieve in any kind of work is insight into what is happening inside us as we do it."

2. Much like online safety-training modules or traffic school courses, computer-based "quests" that issue a micro-credential upon completion can't guarantee that any real learning has taken place.

3. Who determines what competencies are worthy of micro-credentials? How are reviewers selected? How do schools or districts ensure that all teachers have equal access and opportunity to participate in the process?

In the article from Education Week, Brent Maddin, provost of Relay's Graduate School of Education, questions whether micro-credentials atomize teaching to a fault. He asks, "Is there something powerful about how multiple techniques, or moves, or strategies, or competencies move together that are an even better indication of what a teacher can know and do in the classroom?"

The short answer is yes. But there's already a credential for that.

Sources:
Anthony, G., Hunter, J., & Hunter, R. (2015). Prospective teachers development of adaptive expertise. Teaching and Teacher Education, 49, 108–117.
Knight, J., & Learning Forward. (2011). Unmistakable impact: A partnership approach for dramatically improving instruction. Thousand Oaks, Calif: Corwin Press.
Palmer, P. J. (1998). The courage to teach: Exploring the inner landscape of a teacher's life. San Francisco, Calif: Jossey-Bass.

Here's a short video introducing a new course I'm offering with the Center for Professional Development.

Recently I participated in City Summit 2013, a local community-based effort to connect people and their city in new ways, and in the process, foster a sort of re-imagining of what communities might look like. Keynote speaker, John Perkins, recounted his own personal story growing up as the son of a sharecropper in Mississippi in the 1930’s. Through a series of difficult and painful experiences Perkins became conscious of the racial and social injustices faced by African Americans in Mississippi. These experiences fueled his later involvement in the desegregation of Simpson County schools, as well as his work with the broader civil rights movement.

In his keynote, Perkins described the empowering nature of education:

“Education allows us to subdue our environment rather than be subdued by it.”

The Algebra Project

Robert Moses began working with civil rights activists in 1960, and in 1982 founded the Algebra Project, a foundation committed to establishing quality mathematics education for all children. The aim of this foundation and its current work is to increase access to and understanding of algebra in underserved communities, with the expressed conviction that this understanding has significant impact on students’ social and economic futures.

In discussing Moses’ convictions, UC Berkeley Professor Alan Schoenfeld states:

“Who gets to learn mathematics, and the nature of the mathematics that is learned, are matters of consequence.”

In a 2013 interview, Moses described the pivotal role algebra plays in a society increasingly dependent on technology:

Host: “Talk about algebra and what makes it important in general terms. Is it a skill that needs to be acquired for its own sake, or to give students a framework for thinking about other things in different ways?”

Moses: “The information age…has ushered in a quantitative literacy that has put algebra and logic as a necessary literacy for our democracy.”

KQED interview Bob Moses 2.6.2013

On Equity

During the 2013 NCTM Annual Meeting held in Denver, CO, Uri Treisman delivered the Iris M. Carl Equity address. His comments called attention to the empowering nature of mathematics education:

“Mathematics is the biggest determinant in upward social and economic mobility. We need to rebuild our education systems so they allow students to advance. Schools are places where we produce citizens with deep commitments to democratic ideals.”


Mathematics as a tool


We use mathematics as a tool to make sense of and understand the world around us. We need mathematics to help put events and trends into perspective, to look rationally and reasonably at aspects of these events that may not be apparent on the surface. Mathematics helps us go deeper.

Common Core Mathematical Practices emphasize critical thinking as students make sense of mathematics, and as teachers work hard to ensure that students learn to solve real world problems. But what kind of problems do we hope they solve? How will students learn to recognize problems that are in need of solving, and from what perspective will they approach these problems?

We want our students to ask important questions: What’s a reasonable wage? What figures might constitute discriminative behavior? Why are certain communities underserved in terms of assets or resources?

The question here is whether it is enough to deliver a rich mathematics instructional program, or whether we should also strive to help students use mathematics in meaningful ways.

Think about some of the enduring concepts students explore during their school study of mathematics:

number
, counting, 
patterns, 
structure, 
measurement
, data, 
change
, variable, 
function, 
statistics

There are, of course, more. Now think about a current issue or problem that needs attention in your local community, city, or state. You may even want to think globally. Here’s the question:

How many of the above concepts are required to think critically about this issue and understand it? Better yet, how many of these would play a role in any sort of solution to this problem?

Could it be that while students have been asking “When will I ever have to use this?” we’ve been giving many of the wrong answers? Rather than listing jobs that require math skills, perhaps we should revoice that question for students:

Oh, you mean “When will your mathematics understanding intersect an opportunity for meaningful change?”

The world needs mathematical thinkers.