Blog | Summit Mathematics Education Enterprises

What does it mean to be a “mathematician”?

Fri, 29 Jun 2018 09:21:38 -0400

What does it mean to be a “mathematician”? What does it mean to identify oneself as such?

During the last twenty plus years as a mathematics educator, I feel as if I have thought a lot about these two questions. However, I learned recently that I have not thought about them nearly as much about them as I might have supposed.

During a recent book discussion, I was asked to consider the question, “Do you consider yourself to be a mathematician?” Without much thought, I raised my hand in the “no” group – a response which might surprise some people reading this and which also surprised a few of my colleagues in the room.

In the immediate and later discussion of this question that followed, I found myself challenged to articulate why I do not tend to identify myself as a “mathematician”. One idea that came to mind fairly readily is that I know that I associate this word with people whom we might also call “research [or ‘career’ or ‘professional’] mathematicians” – that is, people who make their living exploring mathematical ideas in (often) a formal way. I actually made an intentional career choice toward the end of my undergraduate program not to continue with graduate study in mathematics because I was very passionate about mathematics education in K-12. And, to be honest, I found that even though I was doing well in my mathematics classes (“grade-wise”), I had no desire to continue in what I felt would be even more abstract, theoretical mathematics. I believed that I was capable (as did the mathematics department); I simply chose not to do so.

How many of 13? (or, Which group do you want to be in?)

Fri, 23 Mar 2018 07:58:42 -0400

Your students will have about 13 math teachers from K-12. Will you be one who truly helps them develops growth mindsets?

Most of us have heard about research (granted – it is based on standardized test scores) that says that if a student has ineffective teachers in mathematics for three years in a row, it is nearly impossible for the student ever to “catch up”. I have been thinking about this same idea – not focused on test scores – but in the context of students’ mindsets in mathematics class (though I would argue that test scores are affected by mindsets). What subtle or direct actions and words encourage all students equally, rather than favoring some and “rescuing” others?* How many of 13 teachers does it take to convince a student that he is not capable of achieving much in mathematics? How many of 13 does it take to convince a student otherwise? Which group do you want to be in?

*Here are 10 “easy” teacher moves — that any of us can use at any time — that are very powerful in terms of helping students to believe in their own mathematical thinking (and not rely on the teacher as the ultimate and only authority) — but we have to be consistent about these for them to be effective!

Math in the Movies: Why does Lady Bird throw out her math teacher’s grade book, and what can we do about it?

Fri, 26 Jan 2018 09:45:07 -0500

Having seen the wonderful movie Lady Bird this week (not at all connected with First Lady “Lady Bird” Johnson), I have been thinking about the portrayal of the main character’s high school math class and how it parallels the feelings of so many people about school mathematics. In the scenes involving the class (set in the year 2002), the very pleasant teacher is seen lecturing from an overhead, with students sitting in rows taking notes. There is no real engagement for students in what is happening, and they look incredibly bored. Some students are identified by the well-meaning teacher as being good at math, while others (including Lady Bird) are essentially told the opposite. And Lady Bird questions why she is not good at math even though her father and brother are, while her friend suggests that perhaps she takes after her mom in this regard. The feelings of inefficacy and frustration are palpable. When Lady Bird has a chance, she takes the teacher’s grade book and throws it away in an outside trash can.

Reflection: What it means to be thankful for teachers

Wed, 22 Nov 2017 23:02:09 -0500

I am thankful every day for teachers who think critically and reflectively about students’ learning.

I am thankful for teachers who listen to students without just hearing.

I am thankful for teachers who make professional decisions based on what they know, see, and hear from students.

I am thankful for teachers who learn from each other and from their students.

I am thankful for teachers who see and respond to students’ emotions and experiences.

I am thankful for teachers who communicate with students’ families.

I am thankful for teachers who model respect, compassion, and justice.

I am thankful for teachers who are human beings – because no computer and no set of data could do what is listed above.

Thank you, teachers! You are beyond value! And thank you to all who support teachers!

A challenge: Are you ready to break out of the “test scores” box?

Fri, 13 Oct 2017 11:58:28 -0400

Are you tired of feeling beaten down by test scores? Are you tired of always having to think about “fitting in” a whole laundry list of standards during the year? If you answered “yes” to either of these questions, then I offer a challenge to you – both teachers and administrators. There is real, growing (and in some cases long-term) evidence* that intentional instruction that focuses on the big ideas of the grade level or course, and that focuses on habits of mind like those in the Standards for Mathematical Practice, can deepen students’ learning and understanding while producing laudable test data as well. Of course, “intentional” instruction includes ongoing reflection on the part of the teacher and a purposeful inclusion of ALL students in EVERY element of these classroom practices. As teachers, it means that our primary task in class is to really LISTEN to students and to show them that we honestly believe that their thinking is valuable and important – no matter how sophisticated at that given moment.

Promoting equity in mathematics classrooms

Sun, 20 Aug 2017 12:44:06 -0400

A reflection on what we can do every day to build a better, more equitable classroom and world

As this school year begins, I feel a more profound sense of responsibility and humility as an educator than I have felt in many years. We begin this year facing, in some sense, a different world than we faced at the start of last year – but perhaps the world is not as different as our new awareness of its complexity may be. Perhaps our collective awareness is what has been most changed during the last several months, because teachers deal with extremely complex issues every day of the year.

More than ever, we must acknowledge our opportunity – and obligation – as educators to provide a safe, respect-filled, thoughtful learning environment for EVERY student. We must demonstrate unequivocally that we equally value the thinking and potential of every student, through our words, actions, practices, and policies.

How can we do so in a mathematics classroom? Are you committed to equity, and are you ready to show it?

Suggestions for new standards in grades 1-6

Mon, 16 May 2016 17:03:30 -0400

I invite you to view the following linked files to explore my suggestions for new standards across grades 1-6 that I think would go a long way in helping students to develop deeper understanding…

Part/part/total as the basis for addition/subtraction in grades 1-3

Decomposition of whole numbers in various ways in grades 1-3

Fraction/decimal standards (restructured) across grades 3-6

The way NOT to get better at basketball — or math

Wed, 25 Nov 2015 09:31:48 -0500

Imagine… a basketball coach (let’s say Coach K at Duke) and his team are in the gym. Coach K starts practice by demonstrating a new skill for his team to learn. He asks the two most experienced players on the team to demonstrate it again while the others watch. Then he tells all of the players to take the floor and try the skill. When Coach sees one of the players doing something wrong, he takes the ball from the player, demonstrates the skill again, and then hands the ball back and walks away. After about 15 minutes, he sends most of the team off the court and has his two most experienced players practice the skill for about 10 more minutes, with everyone else watching. Coach K repeats this process with other skills for the rest of practice.

Of course, we know that Coach K would never actually conduct practice like this. Coach K knows well that every player, regardless of experience level, has to be on the court for the whole practice, working on every skill and every part of the game in order to become a better basketball player. He knows that the players with less experience aren’t going to get better by mostly watching.

“I want THAT for my child…” — Creating positive, deep learning experiences in mathematics

Fri, 09 Oct 2015 18:34:52 -0400

Positive, powerful learning experiences for students should be a primary goal of education. When we see students enjoying learning without significant anxiety — when we see students demonstrating deep learning — we get excited. “This is what we want for our students.” “I want that for my child.” What a joy it is to see the potential in young people as they shape their futures in school.

On the other hand, it is easy to be disheartened when we see students consistently feeling frustrated or bored by school experiences. “I don’t want that.” “We can’t let that happen for our children.”

I want everyone to be able to experience the joy that I have seen hundreds of times in the faces of students who have recognized their own deep learning in mathematics. By “deep”, I don’t mean just getting a series of right answers — I mean feeling that their own understanding has been changed substantively — feeling that they have confidence in solving new problems that are not just like 20 recent exercises. That is, we need to lessen mathematics anxiety while deepening learning.

Common Core State Standards and instructional strategies: Not the same things

Tue, 30 Sep 2014 13:22:43 -0400

I have been thinking today about the idea that much of the confusion that parents and community members have when they cite seemingly strange examples of problems related to the Common Core State Standards in Mathematics (CCSS-M) may have to do with the difference between end goals for student learning and the instructional strategies that we may use to reach these goals.

I should add, before proceeding, that there are two types of goals for student learning in the CCCS-M. We have the Standards for Mathematical Content (the “math”, so to speak) and the Standards for Mathematical Practice (the “habits of mind” that support mathematical thinking and problem-solving throughout our lives). Often, effective instructional strategies can relate very closely to the goals in the Standards for Mathematical Practice, so we as teachers need to try to be very clear about what the goals of any given assignment are (and, perhaps, what they are not). This alone may be helpful in easing some frustration on the part of parents.

Teachers learn a great deal by teaching with each other

Mon, 15 Sep 2014 10:37:24 -0400

I begin this entry with the assumption that teachers can improve and enhance their practice over time — in other words, that a teacher on her first day of teaching should by no means be the same teacher who retires thirty or more years later. Certainly, we would expect that just as adults in any other career or profession should, teachers advance in their understanding of their own practice and how to foster better and richer outcomes as time goes on.

However, one major difference in teachers’ opportunities to learn versus such opportunities in most other professions is that teachers rarely see each other actually teach, particularly for any extended or ongoing period(s) of time. And this is not usually a choice on the part of teachers — it is simply a fact, given the typical structure of a school day and year.

Consider other disciplines, professions, or arts in which people learn from each other by actually “practicing” together: athletics, music, law, much modern medicine, and on and on. Even though individuals in these fields must surely practice on their own in order to truly develop their skills and knowledge, they frequently practice together so that they can learn from those who are more experienced or who have different perspectives.

“Quick and easy” versus “for real understanding” — we can’t have it both ways

Fri, 12 Sep 2014 10:47:22 -0400

I tire easily of hearing the claim that a particular educational product or program is “quick and easy” AND that it is effective in developing real understanding — whether this is learning (on the student’s part) or assessing student learning (on the teacher’s part). “Quick and easy” is an enticing phrase, to be sure, but how often in life in general is something that initiates a real change in understanding “quick and easy”? Why would it make sense that this were somehow possible in schools?

We, meaning educators, the general public, and our civil leaders, must accept that if we really want students to be able to apply their learning in real situations (which is one of the major goals of any educational situation), this requires understanding — flexible and varied ways of thinking about and using developed knowledge. Further, if teachers really want to understand what students know so that they can move them further along, this requires time and purposefully designed interaction with students.

How the internet has changed mathematics homework and classwork

Sat, 06 Sep 2014 21:11:16 -0400

It is fairly well recognized among (at least) secondary and college-level mathematics teachers that the problems in essentially every major published textbook can now be found online — with answers. This is even true for some “typical” or “classic” problems that teachers might assign outside of the book. Given this situation, it behooves us as mathematics teachers to think about how to use this situation to our advantage — or, minimally, not allow it to hinder students’ learning.

Particularly, we should be thinking carefully about how to use mathematics class time to assess students’ understanding (formally or informally) so that we are sure that we know best how to support each student. Further, homework assignments could be more focused on providing explanations about concepts or problems — for example, “The answer to #10 is XYZ. Use a diagram and two to three sentences to explain why this makes sense.” Or, “Charlie Brown made the following error in solving problem 6… tell what you think Charlie was thinking as he did this, and explain why this is incorrect and what he should have done.” Of course, this also means that during class, we need to focus on both skill and concept development so that all students — not just the “verbal” few — gain experience answering these kinds of questions.

Information you need to know about HB 597 (potential repeal of the Common Core in Ohio)

Fri, 29 Aug 2014 15:13:46 -0400

I am strongly opposed to HB 597. I share a summary of the major points of the bill below. This bill is currently still in the House Rules and Reference Committee; if it fails in committee, it will not proceed to the full House for a vote. If it passes in committee, it may not be until after the November election that the House votes on the bill.

The bill is written to repeal the Common Core in Ohio (mathematics and language arts). Note that science and social studies are not part of the Common Core, so anything you read or hear in the media that has to do with these content areas is not related of the Common Core (but is often falsely made to seem so).

Essentially, the bill would prohibit the Common Core and the PARCC assessments from being used in Ohio after the 2014-15 school year. For the following two school years, the state would use the old Massachusetts state standards, which Massachusetts has replaced with the Common Core (and a few additional standards that they wanted to include). During those two years, Ohio teams would be created to write standards for Ohio — but these standards must be “distinct and independent” from the standards previously adopted by the State Board. Then, in 2017-18, schools would use these new standards. Keep in mind that this means that in the next four years, Ohio teachers and students would operate under three different sets of standards.

Kim Yoak’s testimony on HB 597 (potential repeal of Common Core in Ohio)

Tue, 26 Aug 2014 18:15:19 -0400

I gave the following testimony to the Ohio House Rules and Reference Committee today. Please be proactive — contact your legislators and let them know your experiences! Click here to see the video.

Good morning Chairman Huffman, Ranking Member Heard, members of the Ohio House Rules and Reference Committee, and guests. Thank you for the opportunity to share my experiences related to the issues presented in House Bill 597.

My name is Kim Yoak. To give you a brief sense of my background: from 2004 until this June, I served as the K-12 Mathematics Consultant for Stow-Munroe Falls City Schools in Summit County. In May, I earned a Ph.D. in Curriculum and Instruction/Mathematics Education from Kent State University. I am a past president of the Ohio Council of Teachers of Mathematics and have participated in projects with the National Council of Teachers of Mathematics, the Ohio Department of Education, and the National Science Foundation. In my position in Stow, I spent at least half of most school days in K-12 mathematics classes, working with teachers and students directly. I also led inservices with K-12 teachers on a regular basis. I am licensed in grades 7 to 12 mathematics, and when I began my career, I taught middle school mathematics for six years. I am now working independently with schools and districts to facilitate professional development for mathematics teachers and, ultimately, mathematics learning for students.

What will you do with your 5 minutes?

Wed, 20 Aug 2014 20:14:44 -0400

There is a commonly stated idea in education that if we are even able to change 10% of what we do each year to better support student learning, we should consider what we could be doing in 10 years. The typical math class at any grade is often about 50 minutes long, give or take. (Some teachers are lucky enough to have double periods; others have to work within 40-minute periods.) Consider: if we could even do something different — something new, something more student-driven — for just 5 minutes of each class this year, we might be on the way to supporting student learning in a whole new way over time. So, if you are a teacher — what will you do with your 5 minutes?

First female recipient of the Fields Medal (world’s top mathematics prize)

Sat, 16 Aug 2014 13:53:24 -0400

Visit this site to read a brief story of Maryam Mirzakhani, the first woman to be awarded the 2014 Fields Medal, similar to the Nobel Prize in the world of mathematics. One particularly interesting point is that she originally wanted to be a writer as a young girl and did not really enjoy mathematics until high school! Her story is so inspiring, and it is incredibly sad that she passed away from cancer at the young age of 40 in July 2017. Still, we continue to move forward as a mathematics community.

Why do so many adults have bad feelings about math?

Sat, 16 Aug 2014 13:24:57 -0400

If there are a few questions that ought to guide our continual improvement process in American mathematics education, this one should be near the top of the list. Why is it that so many people leave school feeling that mathematics is inaccessible, irrelevant, or even scary?

If I were to try to offer a response to these questions, I would suggest that we need to consider the content that we expect all students to learn and master — particularly at the secondary level — and we need to consider, at all levels, what we “teach” students (both explicitly and through our actions) about what is important in mathematics learning.

I am very interested in conducting research (formal or otherwise) on the mathematics that adults use in their daily lives and in various careers. I often wonder if some (not all) of the more specialized mathematics that we teach at the high school level could be delayed for later career-oriented coursework, when it will be much more relevant for the students who must learn it...

A must read: What’s Math Got To Do With It?

Tue, 12 Aug 2014 13:17:44 -0400

Very rarely do books have as much immediate impact on me as the book What’s Math Got To Do With It?, by Dr. Jo Boaler. This book is an engaging read from the first page to the end, drawing on our experiences of mathematics teaching and learning both as students and teachers. Anyone who has taught or learned mathematics, or who knows someone who is teaching or learning mathematics, will benefit from Dr. Boaler’s insights and experiences.

Essentially, Dr. Boaler lays out a very clear, concise argument for rethinking the way that mathematics is taught in schools, based on the idea that most students are not especially successful learning how to solve problems and reason logically in a very teacher-directed, skill-and-drill (what we might call “traditional") learning environment. She describes discussions with teachers and students as well as extensive work in middle and high school classrooms that she has done. She also writes of ways to engage young children (and adults) in fun mathematical activity, both in and out of school, pointing out that this is the kind of activity that often draws people to mathematics instead of pushing them away from it -- the outcome of the school mathematics experience for many, unfortunately.

The Standards for Mathematical Practice - the basis for mathematics teaching and learning

Sat, 09 Aug 2014 08:37:28 -0400

The Standards for Mathematical Practice, which are part of the Common Core State Standards, must be the clear foundation for everything that we do in mathematics classes, from kindergarten through high school and beyond. In essence, they are the mathematical “habits of mind” that we want students to retain and be able to apply when they have forgotten specific mathematical content.

Educators have, for all practical purposes, been able to “ignore” previous sets of practice standards because they were never made explicit as part of standardized testing. However, this is no longer the case, as the PARCC assessments will include a significant number of tasks that are specifically designed to assess students’ application of the Standards for Mathematical Practice. If students are not used to applying these standards on their own while working through problems, they will not be prepared to do so on these high-stakes assessments. Visit this link and this link (both in the PARCC website) to learn more about how these standards will be assessed; for more specific information, see the PDF files that apply to given grade levels and courses.