What will I give you to remember me by?

On Thursday May 9^th, I opened my commencement address to the 2013 graduating class for the School of Education at Loyola University as follows:

Welcome, Reverend President Garanzini, Dean Williams, members of the Deans Party, Faculty, Family, Friends and especially Graduates. It is an honor and a privilege to present this commencement address today.

I am blogging about the experience, because, for me, it was one of those deeply meaningful - end of the year - rituals that as educators gives us such a gift. One season ends. We reflect. We cheer. We laugh. We cry. We lay exhausted from the effort of another great season of teaching and leading. We are on fumes. And yet, we celebrate that wonderful achievement of another year, another season of our lives so to speak – and watch the fruits of our labor (and theirs) walk across the stage.

Like most commencement speakers, I was aware no one is really there to hear my message. The graduates are there to celebrate their triumph - their sustained effort and work. And, as in so many cases the village of family and friends that love them and helped them walk across that stage, are there too.  

And funny thing about this annual ritual: We realize that life always plays in a forward direction; there is no rewind button. I watched them walk across that stage to get that hard fought for diploma and wondered, What do we give them to remember us by?

In my message – you can get an abridged version of it at SmartBlog on Education - I suggested four categories of pursuits for knowing if you are truly making a difference.

First, did you pay attention to others deeply?

Is it possible there are individuals you could have loved more deeply or encouraged more often?  “Someday I’ll get around to noticing and paying attention to others better,” you say. But someday never comes.

Second, did you become a servant leader?  

Robert Greenleaf wrote:   

The servant leader is servant first . . . it begins with the natural feeling that one wants to serve.  The best test, and the most difficult to administer, is: Do those served grow as persons? Do they, while being served, become healthier, wiser, freer, more autonomous, more likely themselves to become servants? And, what is the effect on the least privileged in society: Will they benefit or, at least, not be further deprived?

Long after you have left the building, will there be a positive residue of service that permeates from the impact of your work?

Third, did you forgive others gracefully?

The very nature of communication among educators during a school year guarantees feelings will be hurt, someone will be wounded, and grace will be needed.

Grace wins out in the workplace when we set down the grudges we are carrying around.

Grace wins when we use forgiveness to help others become better people.

Fourth, did you live a reflective, balanced high-energy life?

The pace of your teaching, leading and serving days will leave you emotionally and physically exhausted. And the more tired you are, the less positive energy you will have for the demands of the fast-paced work that lies ahead. 

The key is to get better at strategic disengagement:  low positive energy reflection time activities. When you become a more reflective practitioner, you avoid the malady of job fatigue: low energy, disengagement from work, superficial effort, and poor judgment.

Here is how I finished my address:

As a Loyola graduate today, you will choose and build the story of how you will be remembered every day, one brick at a time. Your teaching. Your serving, your leading, Your story. May those of us be blessed enough to have known you and your story, may we never forget it.

So, what was your story this year? What did you give us to remember you by in this season of your life? 

Finding Formative Assessment while Checking for Understanding!

It’s April and that means….

Mathematics educators from across the U.S and Canada (and parts of the world) come to our national meetings for mathematics. I have been attending the National Council Supervisors of Mathematics (NCSM – mathedleadeship.org) and the National Council Teachers of Mathematics (NCTM  - nctm.org) meetings every year since 1980. I have colleagues who have been attending as far back as 1961 – but I won’t name them here!

The annual meetings provide a time and an opportunity every year for us to refresh and renew in our knowledge development and our relationships with so many mathematics educators and leaders facing the same issues and problems we face in our local schools.

I had the opportunity to speak at both conferences this past week and I am grateful to the many of you that attended those sessions. It means a lot to me and always inspires and surprises me that so many would choose those sessions when there are other wonderful choices as well.

I promised all in attendance that I would post my presentations from these sessions. Here they are. Two one is listed under NCSM and one under NCTM. Just click on the icon and you will find the pdf's there.

Of course with the CCSS Assessments looming ahead in just two short years (and the Texas TEKS on top of the Texas teachers) it seemed that so many sessions focused on Assessment this year. In some cases Formative Assessment as it applies to in-class instruction, and in other cases Formative Assessment as it applies to the purpose and uses of summative tests.

As I listened and participated in so many sessions during the five days, it occurred to me, that the CCSS M and more specifically, the Mathematical Practices call us to a new standard of K-12 classroom lesson design. When I was teaching in the 80’s and 90’s there was pressure on me, to teach using small step instruction, with lots and lots of small group discourse. The primary management tool for this was called Cooperative Learning and the instructional vision for it, was based to some extent in Madeline Hunters’ notion of Guided Practice.

Yet, cooperative learning and guided practice were often misused and abused ideas about what good mathematics instruction was to become. It generally missed out on the deep discussions student peers were to have with one another and it did not develop the deep commitment teachers were to make toward providing formative feedback to students during those discussions. 

In some ways my role as a teacher during those two decades was to check for student understanding, but only that: 

Check for understanding   

I wasn’t expected – as the teacher  - to do anything with those checks. Nor were the students expected to do much either. And as we entered into the first decade of the 2000’s – many of us digressed back to the worse thing we could do: Check for understanding from the front of the room using whole group discourse – mostly with the chosen few who responded to our questions – and perhaps even worse – only check for understanding on low cognitive demand tasks.

Ouch

And why did we digress back into 1980 and 1990 habits despite the PSSM process standards call from NCTM and the adaptive reasoning call from the National Research Council?

Because it was easy. More efficient. Less pressure to prepare when crunched for time, and in some cases it fed teacher malaise or laziness toward their craft.

But the CCSS M and the Mathematical Practices expectations for student demonstrations of understanding and proficiency in these standards is exactly the kick-start we need to stop the drift. Stop the malaise. Stop the practice of checking for understanding in a way that does not promote student learning.

Here is what we now know

In the CCSS M era, we will need to use formative assessment in the classroom correctly. To do so means:

1. We use well-crafted mathematical tasks

2. We pose them for student to work on using solution pathways as peers

(Note: These problems or tasks can take 2 minutes, 20 minutes, 2 days, etc… time length can and should vary).

3. During these small group peer to peer opportunities, we monitor student discussions and not only check for understanding, but also 

4. We provide formative feedback based on what those checks reveal. We provide students with

5. Differentiated feedback - scaffolding/assessing questions  - that help students to get unstuck as a team, and carry on with a productive dialogue

OR

6. We provide advancement and assessment questions that guide some student teams into deeper levels of thought then originally expected.

And here is the kicker:

Unless the students – during these small group peer-to-peer moments – take action on the feedback you give them then the formative process is empty.

This means that during the classroom period or mathematics time in an elementary class, you must pose some problems that require more complex levels of student reasoning, you must go out among the student teams and monitor their work and understanding, you must give each team feedback and help them stay actively engaged in elements of the problem, and then, you must make sure they take actual action on the problem.

That is a very tall task. The CCSSM will demand a lot from us every day, for the rest of this decade. But we can do it. We must do it. Students deserve to learn mathematics with understanding. In our 5 book PD series Common Core Mathematics in a PLC at Work™, we provide a simple Lesson Planning Design tool for you to use toward this end. I hope you can make it your own.

I wish you the best in this formative assessment pursuit  - it is so much deeper than what was required of us just a decade ago, as math teachers. Help your colleagues too. We will need confidence and skill to become effective 21^st Century Mathematics Teachers. 

Leading and Understanding The CCSS Mathematical Practices!

One of the unique features of the Common Core Standards for Mathematics is the focus on Content standards and Process standards.  These process standards (there are 8 of them) are not a checklist of teacher to-dos, but rather they are proficiencies for students to experience and demonstrate as they master the content standards.

Each of the eight Standards for Mathematical Practice begins with three words—Mathematically proficient students. This language establishes an expectation for evidence of student growth toward proficiency in each of these eight practices as part of the K–12 mathematics learning experience.

And

The Standards for Mathematical Practice describe what students are doing as they engage in learning the CCSS for mathematics content standards. How should students engage with mathematics tasks and interact with their fellow students? How well do teachers develop students’ engagement in mathematics reflecting the CCSS Mathematical Practices?

One of the fundamental shifts of the Common Core for Mathematics is that how students learn the mathematics, is now as important as what students learn. And, as a school leader, you need to both support (celebrate) and hold accountable  teacher lesson planning design and implementation that intentionally plans for these student proficiencies. 

Over the next few blogs, I will outline ideas for each of the eight mathematical practices around two critical questions:

1. What is the intent of each Mathematical practice?

2. How will you ensure each collaborative team addresses the CCSS Mathematical practice on a unit-by-unit basis?

It is up to you and your teachers to shift instruction and provide evidence that students are actually developing each practice.

Mathematical Practice 1: Make Sense of Problems and Persevere in Solving Them

Mathematical Practice 1, “Make sense of problems and persevere in solving them,” refers to the ability of students to explain to themselves (and others) the meaning of a mathematical task or problem and look for entry points to its solution (NGA & CCSSO, 2010, p. 5).

What Is the Intent of Mathematical Practice 1?

Problem solving is one of the hallmarks of mathematics and is the essence of doing mathematics (NCTM, 1989). When students are engaged in problem solving, it means they are drawing on their understanding of mathematical concepts and procedures with the goal to reach a successful response to the problem.

As you study the expectations for Mathematical Practice 1, you will notice several areas for student proficiency including:

1. Students make conjectures about the meaning of a solution and plan a solution pathway.

2. Students try special cases or simpler forms to gain insight (they hypothesize and test conjectures).

3. Students monitor and evaluate their progress and discuss with others.

4. Students understand multiple approaches and ask the question, “Does this solu­tion make sense?”

5. Students explain correspondences between equations, tables, graphs, verbal descriptions, and data and search for regularity, patterns, or trends. 

Successful problem solving does not mean that students will always conclude with the correct response to a problem, but rather that students will undertake a genuine effort to engage in the problem-solving process, drawing on learning resources described in the other practices such as appropriate tools, using their prior knowledge, engaging in math­ematical discourse with other students, and asking questions to make progress in the problem solving process. Successful problem solvers also recognize that powerful learning can be experienced even when an appropriate answer to a problem ultimately evades the student.

How Can Collaborative Teams Address Mathematical Practice 1?

Teachers play the important role in supporting students’ ability to make sense of problems and persevere in solving them. The first of these roles is the presentation of appropriate problems or tasks for students to solve. While it seems that appropriate is subjective, there are six questions you can present to teachers for discussion within their collaborative teams when planning lessons to assess the qual­ity of problem solving within a common or shared mathematical task.

As we develop common tasks and problems to be used during the unit, we should consider:

1. Is the problem interesting to students?

2. Does the problem involve meaningful mathematics?

3. Does the problem provide an opportunity for students to apply and extend mathematics?

4. Is the problem challenging for students? Does it apply a complexity of reasoning at the DOK level 3 or 4?

5. Does the problem support the use of multiple strategies or solution pathways?

6. Will students’ interactions with the problem and peers reveal information about their mathematics understanding?

Observing students’ interactions with a mathematical task (for example, students’ work, discourse, tools, and representations) will provide information about how their thinking is hindered or evolving by interaction with the problem or task selected. This list of questions is not exhaustive, but it is a beginning step toward examining problems for the potential benefit they can provide for advancing students’ mathematical problem solving and learning.

Your leadership role is to ensure teachers work in collaborative teams to discuss how to help students understand that the answer is not the final step in the problem-solving process. A great deal of mathematical learning can happen when students are guided to explain and justify processes and check the reasonableness of the solution. After teaching lessons within the unit, teachers on the team should ask:

“Is there evidence that students are learning other ways of solving the problem? Is there evidence that students are making and learning mathematical connections to other problems and mathematical connec­tions as they persevere in solving the problem?”

As a school leader, you must focus deliberate attention on implementing the CCSS Mathematical Practices, part of your challenge will be to envision and teach what the practices "look and sound" like in the classroom as part of instruction.

The student tasks teachers design, the questions they ask in the classroom, and the discourse in which students participate will all combine to advance students’ abilities to engage with peers in the Mathematical Practices.

If you lead and teach in a Common Core State these practices are not optional. If you don’t lead and teach in a Common Core State (Texas, etc) these practices are not optional. I wish you the best in this non-optional pursuit! 

Good Instruction: Thinking About 1990 in 2013

In the 1990 NCTM Yearbook on Teaching and Learning Mathematics in the 1990's, I wrote a Chapter titled: Effective Mathematics Teaching, One Perspective. And in that article, one section was titled Presenting the Content and Checking for Understanding. 

On the eve of the 2013-2014 and 2014-2015 launch of the Common Core those words, written 23 years ago, apply more than ever today. Our language has changed a bit, but remember in my December blog, when I claimed that you can't effectively check for understanding from the front of the classroom? This article, in its own way, supported that claim, with a few caveats. Although presented with minor edits, it represents the commitment to mathematics instruction we made at Stevenson during the 1990's. A commitment that is now required for all of us, because of the expectations for how children learn mathematics as presented by the Common Core and the CCSS assessments.

In this blog, I present part of that Chapter from 1990 - in italics.

The move into the presentation of content invites the question, "How do I check for student understanding during the presentation to class? Most teachers are very good at modeling examples, but tend to stand at the front of the classroom and check for understanding by using such verbal cues as "Did I go too fast for you?" Does everyone see that?" "Isn't this an easy one?" "Okay?" "Who doesn't understand that?" Often included is the very rhetorical, "Any questions?" 

These particular cues set up two very counterproductive conditions in the classroom: 

1. The teacher makes the false assumption that no response from the students indicates that everything is understood and it is "Okay" to continue. 

2. The students develop a sense of lowered self-esteem if they do respond to them, since it is an admission in front of (all) their peers that something is not okay. 

Thus, teachers need to develop effective techniques for checking for students' understanding (these checks also give students an opportunity for reflection with their peers on the content being learned).

 There are three effective ways to check for understanding. 

1. Reflective [Student] Discussions During the Presentation

On complex problems (Today we would say DOK 3 or 4) the teacher could help students set up the initial investigation into the problem, but then allow them time time to work together to discuss strategies for solving it. This is a good time to circulate among the students to find out if they understand the set up of the problem (today we might say "solution pathways") and possess the necessary skills for solving it. While walking around, the teacher is giving and receiving feedback and checking for understanding (Today we would say "provides formative feedback").  

2. Effective Questioning 

Note: It is in this section of the 1990 article that I attempt to describe one way you might be able to check for understanding from the front of the classroom. However, it is very very difficult to do really well.

Effective teachers use questioning strategies that encourage all students to consider the questions they are asking. An effective questioning cycle must require all students to listen actively both to the question as well as to other students' responses. A questioning cycle likely to result in this active student engagement includes the following four steps. 

1. Pose the question 
2. Provide "Wait time" after each question to prevent any student callouts. 
3. Select students randomly, making certain to call on all students. Call on volunteers as well as nonvolunteers. 
4. Redirect individual student responses to other students for their judgement of correctness or for an extension of an answer. 

During whole group discourse from the front of the classroom, some students are reluctant to wait to be called on and like to call out an answer or response. Student callouts are disruptive to the flow of the classroom dialogue and allow certain students to dominate the discourse and force the direction of the classroom focus. Callouts also move more passive students to disengage. 

A phrase that encourages wait time is to immediately follow a question with "Raise your hand when you are reasonably sure of the answer". The questioning sequence provided below provides an example of an effective "Front of the Classroom" questioning cycle. 

Note: The names I used in this dialogue are my parents and at the time young children!

T: Class. Can you provide me with an example of a triangle with an Area of 12cm^2? 
Please draw and label a diagram on your papers and raise your hand to respond. (Teacher monitors and walks around the room as students hands are raised) 

T: Only Jessica and Adam have such a triangle? (This buys more wait time) Are there more? Three hands ? Four Hands? Anyone else? (Total Wait time is 8-10 Seconds or more) 

T: Okay, Roy. I noticed (when I was walking around) you chose a right triangle. Please explain your diagram to the class. (Roy did not have his hand up). 

R: I drew a right triangle with legs of 3cm and 8cm.

T: How many of you agree with Roy's example? Raise your hands! Who disagrees with Roy? Who is listening to what Roy just said? (This forces other students to pay attention and engage in Roy's response)

T: Who can prove or disprove Roy's assertion.... Connie? (Connie had her hand up) 

C: In a right triangle, the legs represent the base and the height. Thus, A= 1/2bh or A=1/2(8)(3) which is 12cm^2, so I think Roy forgot to divide by 2" 

T: Roy do you understand Connie's Assertion? Do you agree with her? (And Roy responds) 

T: Thank you! As I walked around the room, I noticed all of you used a right triangle. Can you think of an example that is not a right triangle? (Here this dialogue is best continued in a well-managed small group peer to peer discussion as the teacher tours the room and listens in). 

Effective questioning from the front of the classroom can no longer be our primary method of "Checking for Student Understanding". As I mentioned last month it should be no more than 35% of your classroom time. However, if you are going to use whole group discourse to determine if students are "Okay" and "Understand", then at least use a questioning cycle that:

Increases wait time, severely limits student callouts, and promotes group feedback to a students' response with positive whole group student feedback on the questions you ask your class. 

Mathematics classrooms of the 1990's were dominated by teacher talk, and often ineffective and false checks for understanding from the front of the classroom. Today, in 2013, mathematics classrooms should be dominated by the use of effective problems and tasks that allow for deep peer to peer discussions as the teacher checks for understanding and provides the type of formative assessment feedback that engages all students in learning. This was actually the third way to effectively check for understanding in the classroom that I described in the 1990 article.

Madeline Hunter called it Guided Practice, Spencer Kagan called it Cooperative Learning, James Popham and Dylan William call it Formative Assessment and the CCSS  calls it Developing deep student understanding through the Mathematical Practices. I call it great instruction that respects student engaged learning as an essential classroom tool for feedback to learning.  

I wish you well in that pursuit.

Measuring Your Success in 2012!

At the risk, of being a bit redundant, I am "Re-Posting" my blog from January 2nd, 2012, today. It is provided below. Why do this? First, my blog readership has doubled in 2012. So, I figure from time to time some of the old posts may have some value.

Second, at the end of that 1st post for 2012, I stated:

So, as we enter in 2012, as you celebrate the ending of one semester, and the beginning of another, please keep in mind it is the community members that matter. Celebrate their triumphs, embrace their tragedies, help them grow. Take pictures of them, post those pictures everywhere you can. And then watch the years flow by. Because in a blink, it will be 2013, and you will have to ask, "How did I do in 2012? How did I serve and lead the members of my home and professional families?"

And only you can measure your success as a family member in 2012.

Well, that blink is here. It is 2013 in 2 days. How did 2012 go for you? How did the celebrations of those in your work and personal "Families" go?

2012 left me more accomplished, but exhausted. It was intense, furious and fast paced with little time to fully enjoy those in my life that I trust and love so much - both my professional friends and my personal family members. I think in 2012 I took from them more than I gave. It is both a point of reflection and a point of grace that I plan to work on in 2013.

And, as is generally the case for all of us, my success as a fully functioning "Family" member, suffered because of my inability to find the necessary Quadrant II time, to be successful. So, like me, enjoy the posting from a year ago, and then challenge yourself to ask, "How will I measure my success as a family member in 2013?


Posting from Jan. 2nd, 2012:

Like many of the readers of this blog, my family (which at this stage of life has various definitions and extended members) spent parts of this holiday season together. Annual family gatherings are often filled with both joy and sadness, tragedy and triumph, reflection and action, fear and hope as one year ends and another begins.

In some sense, our family gatherings represent the same feelings and emotions that we experience in our professional families as well. If you are a teacher, your students are part of your school "family" and your colleagues are part of that family too. If you are a coach your team is part of your school "family" and your fellow coaches will spend more time with you during the season than your "at home" family. If your are a school administrator or district leader, your "family" widens as you steward the members of the school community as well. It becomes a pretty big family to be part of and to understand.

So, as we were ending our family vacation time on January 1st, we sat around the TV, and began a 45 minute slideshow "walk" through the pictures of our time together, taken by various "keepers" of the camera. As we sat in the living room, and watched the pictures flow by, it was interesting to observe family member reactions. The first 10 minutes of our slideshow was mostly pictures that looked like this:

You know, the very nice scenic views that when you get home you say, "I took 122 pictures of that?" Maybe two would have been sufficient. The reaction around the room was polite, but a bit bored. Then a picture of our two daughters playing xbox 360 skiing (part of a family competition) with legs flailing in the air and arms spread out using imaginary poles, heads knocking together and both of them laughing hysterically - caused a major eruption of laughter, pointing and energy from our gathering. (Note: I cannot supply the picture here as I have yet to secure permission from our two daughters!)

I found myself wondering, what is it about our pictures that as soon as people (especially the members of our extended families) show up in them, a level of new energy and emotion is released? It occurred to me, that our life, our work, our family, is rarely if ever about the place as much as it is about the people - and our experiences with those people, both good and bad. It is the people that make the place have purpose and meaning, passion and emotion, joy and heartache. Without the people - the place becomes empty space.

I first remember experiencing this feeling during my early days as a high school basketball coach at West Chicago Community High School. We had just lost a close home game with a conference rival, and I was a bit distraught over the loss. Once the team members (one of my many families) had gone home, and the coaches too, I decided to walk back into the gym, and just stand in the middle of the gym floor. I wasn't sure it would make me feel any better, but I wanted to capture a picture in my mind of the emotion displayed by 1000+ people just an hour ago: The heartache and the joy of participating in something.

I was struck by the emptiness of the space. The building in the dark, was just that - a nice facility, a nice place - but no emotion no energy. The building, that gym, needed people for it to matter. It needed people that cared about their team, that cared about risk and success. That understood how wins and losses matter only briefly as a measure of success, but real success would reveal itself in whom all of those young men and women would become.

In 12 years of coaching I had taken a picture of every team that was part of my school family. In every case, the years and the records (even the good years) just sort of blend together. But I can always tell you about the year my players asked me to design a "Fibonacci" defense for them (I was a math teacher and we also had the Euclid zone press). Or the year that I dubbed one of our players the X-factor. Or the year that several of my players had significant tragedy in their lives - including the house burning to the ground for one player during the season. And it was our family reaction and response to these events that made the season a success. It is and will always be about the people in our "families" and the relationships built  around them.

When I became director of mathematics and science at Stevenson, every fall (at open house) I would insist that we all "dress up" and get together in the commons area for a "team picture". As we grew the picture had quite a few teachers in it (up to 85 at one point) but I loved placing the team picture on my office door every year. As the years unfolded, of course our "family" members changed in the picture. New additions and departures for many different reasons, would impact the picture. No matter, the "Commons" isn't what made the picture work for me, it was the energy of the great people in the picture that mattered. People that just like me, were trying very hard every day to help their student family - to become positive community members.

And now you enter in 2013 - another year will become part of your legacy. Celebrate thetriumphs of others, embrace their tragedies, help them grow. Watch the years flow by. Because in a blink, it will be 2014, and you will have to ask, "How did I do in 2013? How did I serve and lead the members of my home and professional families?"

And only you can measure your success as a family member in 2012  2013! See - the years really do start to stack up!

Happy New Year!