Less is Sometimes More

I had a meeting today...actually I had two really big meetings today; one with a newly appointed principal, and another with a group of teachers.  Both groups having the same focus...how do we get our students to do better on the state exams?  I had some thoughts, but what they all really wanted was a "quick fix" to a very deep and systemic problem.  It is kind of like using Band-Aids for a festering, and pus-filled wound; not effective and in the long term...deadly.

You know one of the biggest problems our students have...besides our antiquated educational structure...it is expressing, showing, and explaining their thinking.  As educators, we generally rebel against expressing our thinking.  Expressing our thinking requires work, sometimes mental, emotional, and/or physical.  Showing our thinking takes effort.  Explaining our thinking may leave us open to criticism.  Expressing our thinking is sometimes a slow and incomplete process that requires us to revisit ideas.  When do we do that (expressing, showing, and explaining their thinking) for ourselves? How can we do that (expressing, showing, and explaining their thinking) for our students?

Consistently using conceptually rich, academically rigorous problems can be a pathway to expressing thinking, but it begins with teachers being willing to embrace and express his/her own thinking publicly and in writing.

Step 1: Choose or create a problem. 

Step 2: Do the problem with your colleagues and use multiple representations to show your thinking. 

Step 3: Identify the "big ideas," math standards, and concepts/skills addressed. 

Step 4: Outline the various strategies that can be used to show and resolve the problem.

Step 5: Identify the possible student misconceptions. 

Step 6: Express what you would like to see in your student's solutions.

Step 7: What questions might you ask students to help them deepen their thinking and understanding?

By following these aforementioned steps, teachers will have a clear understanding of what students are thinking as expressed in their work.  Teachers will also have a better road map of student understanding and of how to move them to the next level.

Now what is meant by conceptually rich, academically rigorous problems?  Compare the two tasks below and think about which question allows you find a solution by taking multiple paths?  Which question pushes your thinking via the mathematical connections that you make?  What are the mathematical concepts involved? How might the concepts involved, change by grade?  Can you show multiple representations for either task?

Task #1: Write a number sentence using at least four different numbers for which 0.86 is the answer. (Source: OPEN-ENDED ASSESSMENT IN MATH by Heinemann)

Task #2: Solve the problem: 0.23 + 4.5 - 1.4 + .25

Follow-up:

• Select Task 1 or 2
• Complete Steps 1 to 7
• Group discussion: Ms. Jones, an educator, states, "While task #1 is richer, my students would not see that kind of question on the test. Besides, my kids would just get confused with all the different solution options. On the test there is only one correct answer."
• How would you respond to Ms. Jones?

The Power of Collaborative Learning Communities

When was the last time you met with your fellow teachers to discuss your instructional strategies for test preparation? When was the last time that you looked at and examined student work in relationship to how they might perform in a testing setting?  I am currently participating in a training with Sandi Everlove, the founder of TeachFirst, and today we are focused on the value and necessity of professional learning communities.  One of the big ideas that is coming out is the focus on student learning as a way to examine our own instruction.  And in order to do that we need to do a few things...in a 1995 article, "Building Professional Learning Communities" by Sharon Kruse, five critical elements were identified: 1) reflective dialogue; 2) de-privatization of teaching; 3) collective on student learning; 4) collaboration; and 5) shared norms and values.  The podcast below focuses on two of those elements: reflective dialogue and the de-privatization of teaching and how that might apply to developing test-savvy students.

Additional resources:

• All Things PLC
• The Center for Comprehensive School Reform and Improvement
• Productive Group Work: How to Engage Students, Build Teamwork, and Promote Understanding by Nancy Frey, Douglas Fisher & Sandi Everlove

Gather a few colleagues, take a look at the following example of student work and take a moment to comment.  The task is open-ended and would not be found on standardized exam currently, but look at what the student did.  What does this response indicate about how this student might respond to an extended/constructed response question on a standardized exam?  In your conversation, focus on the following questions:

1. What does this student know? 
2. What grade-level standards are being addressed? What are not? 
3. What might be somethings that you would do in your classroom to help this student become more test-savvy? Think about the Mathematical Practices as indicated in the Common Core Math Standards.

"Bowls of Apples" task from Exemplars Math

Test-Savvy Principal #3: Collaboration

In James Suroweicki's book, The Wisdom of Crowds, he talks about how groups of people who are focused on a task can often come up with or develop better answers or closer approximations, than if they were working independently.  He discusses that how many times the task of finding solutions to problems that pertain to a specific area of specialization are left to the experts of that field.  For example, economists discuss how to reduce our national debt and get us out of this recession, but homemakers are not invited to these conversations.  But Suroweicki argues that we need a wide variety of individually who have a vested interest in a particular topic to contribute to the conversation in order to develop better, more meaningful answers.  Listen to his 2004 interview with NPR News Radio. 

How does this apply to creating test-savvy test takers?  Simply put, while taking a standardized exams is an independent endeavor, the preparation needs to be a collaborative process.  Students need to have opportunities to listen to the ideas of others, but remain firm enough to state their point and understanding.  It is through the process of collaboration that we generate new and better ideas, solutions and products.  In order to effectively collaborate we need to 1) provide students time and training needed to document their initial thoughts and solutions to a problem; 2) provide a venue where all students can compile, share, and evaluate the data gathered; and 3) encourage students to voice their opinions and support them with facts.  Think about how you are fostering true collaboration, not just getting the students to think like you.

Our Culture of Testing...Can Creativity Flourish?

Every year I watch the same cycle...either educators who worry about testing from day one or the ones who worry about testing six weeks prior to the date of THE TEST.  Either way the results are the same...educators worry about standardized testing.  I was reading a funny, well thought out story about standardized testing, Testing Miss Malarkey.  The story is presented from the point-of-view of the students, the actual test-takers.  They mention how the adults and even their parents started to act strange and school as they had know it...changed because of THE TEST.  In art class, they made posters about how to fill-in the circles on the test in a "good, clean, neat and nice" fashion.  In gym class, they began to practice yoga to prepare their "minds and bodies."  Parents started giving their kids power bars to build the brain.  On the day of the actual test, sick, nauseated teachers overran the nurse’s office.  And strangely enough, after the test things returned to normal...leaving the students to conclude, "THE TEST really wasn't that important after all."

The fact is we do a disservice to our students and ourselves by negating THE TEST on the surface, while allowing our actions to show that we are deeply, DEEPLY vested in testing.  Maybe it is because we do not have a better system.  Maybe we are scared to enact a better system.  Whatever the reason, if we accept standardized testing, either by conscious choice or by default, then we need to acknowledge it, accept it, BUT allow for creativity and critical thinking despite it!

The video below focuses on creativity in education.  The test-savvy philosophy advocates creativity and allowing students to be partners in the creation of content for the classroom.

   

Check out his book: The Element: How Finding Your Passion Changes Everything by Ken Robinson

Writing in Math

Getting students to write effectively and coherently is a challenge.  A challenge many educators feel ill equipped to tackle for a few reasons. First, educators themselves may be uncomfortable with writing, especially in the area of mathematics.  Much of our experiences with math has been very procedurally based using numeric representations that were not tied to any real-world connections.  Second, writing, like reading, involves many subtle steps and seemingly undefined nuances.  The old adage of, "we learn to write by writing," does not seem to translate to student growth in the classroom.  Third, many students have adopted the sentiment that math class is not for writing or that writing in math is hard and boring.

I once heard an author say, "I don't know what I am thinking, until I write it down."  In order to best educate our students for the needs of the 21st century, we have to...it is essential that they know how to articulate their thinking via the communication tool of writing.  So how do we do this?  How do we develop better writers in math class?  This weeks podcast focuses on "7 Steps Educators Can Take to Improve Student Writing in Math" and check out the YouTube Search Story on Writing in Math.

Check out these additional resources:

1. Six Steps to Better Vocabulary Instruction by Marzano (online in Educational Leadership)
2. Closing the Vocabulary Gap by Jane L. David (online in Educational Leadership)
3. Using Writing in Math to Deepen Student Learning by MCREL
4. Systematic Vocabulary Instruction by MCREL
5. Inside Words by Janet Allen
6. Writing in Math Class by Marilyn Burns
7. From Reading to Math by Maggie Siena
8. Writing to Learn Mathematics: Strategies That Work, K-12  by Joan Countryman (recommended by Dr. Janine Stewart)
9. Writing Math Research Papers: A Guide for Students and Instructors by Robert Gerver (recommended by Dr. Janine Stewart)

Test-Savvy Principal #2: Accountable Talk

The 2nd Test-Savvy Principle is Accountable Talk.  Accountable Talk is one of the nine researched-based Principles of Learning as categorized by the Institute for Learning (IFL) at the University of Pittsburgh.  IFL states that, "The Principles of Learning are condensed theoretical statements summarizing decades of learning research. They are designed to help educators analyze the quality of instruction and opportunities for learning that they offer to students." Accountable Talk is about talking to others about our work and being able to clarifying our thinking about a given topic.  The one who is talking is the one who is learning or clarifying their thinking.  In many classrooms, teachers do much of the talking, thus much of learning.  In the Voicethread posted below, we will look at Accountable talk in action.  The test-savvy strategy being used the is Word Problem Rework.  The student is in the 3rd grade.  Consider: 1) What does the student know about the concept?  2) Where is the student on the continuum of learning from concrete to representational to abstract?  3) What misconceptions is she student grappling with? 4) If you were her instructor, what might your next steps be?  Please note, this is the students first "rework" and her first Voicethread.  Please feel free to leave a comment (feedback) for the student, as she will learn from what others have to say.

Motivating Students

Just watched a video lecture by Daniel Pink as he spoke at the TED conference in July, 2009.  Please watch the video and ponder the following question:  How can we apply the ideas of intrinsic motivation to student learning?

Test-Savvy Principle #1: Student Ownership

This is crunch time for many schools.  They are entering the "test triage" zone.  Every year around this time I see educators pull out the traditional test prep book, give simulations exams and frantically try to figure out strategies to help students do well on standardized exams.  Every year it is the same cycle...give lip service to the exams the first half of the school year and ignoring data.  Then as exams get closer we test the daylights out of students, pinpointing their areas of weakness and enact various extra/enrichment programs and provide additional resources to "help" students succeed on the upcoming exams.  We lament about all we have done, but the students still don't get it or they are not paying attention.  ENOUGH!  ENOUGH IS ENOUGH!  We need to teach differently!  Students need to take ownership of their learning.  This podcast is about using test-savvy strategies to provide opportunities and structures that allow and foster student ownership of learning.  Test-Savvy Principle #1: Student Ownership

What is Test-Savviness?

In our world of high-stakes testing many teachers cannot escape the lure of teaching to the test. But the term "teaching" conveys that in order to teach, learning must have taken place on the part of those being taught. But year-after-year teacher get a new crop of students whom they say did not retain any information from the previous school year. It that is the case, were the students taught? Did learning occur? Did the teaching that took place meet the needs of the learner? Often times this conversation takes a back seat to preparation of standardized exams.

 
I have developed a set of classroom strategies for developing test-savvy math students. I believe that we can use research-based instructional strategies that promotes higher order thinking skills using, plus test prep. The result is "test-savviness". Test-savviness in math is about knowing and understanding three things:
 
1. math content and understanding how the content might be assessed;
2. the test, its mechanics and procedures; and
3. ones own personal strengths and challenges.
 
Each week, I will preview one of the test-savvy math principles (student ownership, accountable talk, collaboration, error analysis and tapping into prior knowledge) and discuss how a strategy can be applied to mathematics instruction. When used consistently, the result are students who are not only better prepared for high-stakes exams in math, but also students who are better prepared for life.