What are you talking about in your math classroom?

At our first department meeting I shared a summary on the topic of orchestrating productive mathematics discussions in the classroom.  This was based on the book 5 Practices for Orchestrating Productive Mathematics Discussions (Smith and Stein 2011) available from NCTM.  The reason for sharing such a topic is because the idea is interwoven throughout everything our district, state, and nation are striving for within our profession.  The CCSS focus on the 8 standards for mathematical practice; the ACT Framework encourages student discourse; and the REIL Teacher Observation Instrument has an entire rubric dedicated to the concept of student engagement.

Over the course of the school year I will be posting on the various practices presented in the book that will help us orchestrate productive mathematics discussions.  The argument is made in the introduction of the book that our country needs highly trained workers who can wrestle with complex problems.  It is stated that research tells us that complex knowledge and skills are learned through verbal interaction.  It also argues that teachers must learn how to support our students as they engage with and discuss their solutions to cognitively challenging tasks.

Given that framework, let us take a look at laying the groundwork for productive mathematics discussions. 

Before we look at the five practices we must first consider the foundation to the entire process: Setting Goals and Selecting Tasks.  The bottom line is that teachers must first establish a clear and specific goal with respect to the mathematics to be learned and then select a high-level mathematical task.

Choosing a clear and specific goal - 

The following are three different goal statements with varying levels of clarity and specificity:

•  Students will learn the Pythagorean theorem (c² = a² + b²)
• Students will be able to use the Pythagorean theorem (c² = a² + b²) to solve a series of missing value problems.
• Students will recognize that the area of the square built on the hypotenuse of  a right triangle is equal to the sum of the areas of the squares built on the legs and will conjecture that c² = a² + b².

The progression of the three goals illustrates the degree of specificity a goal can have.  A learning goal should provide the teacher with a clear instructional target that can guide the selection of activities and the use of the five practices.  Try rewriting a learning objective so that it is more explicit; and think how the more explicit goal could influence the way in which you plan or teach the lesson.  

Selecting a high-level mathematical task – 

The table below can be used in analyzing the potential of the mathematical tasks that you may choose.  Try to select tasks that meet the criteria on the right side of the chart.

Different tasks provide for different student opportunities.  Rote practice of standardized procedures leads to one type of student thinking.  Tasks that demand engagement with concepts and that stimulate students to make connections lead to another type of student thinking.  Are you providing your students opportunities to engage in high-level tasks?  Can you identify tasks in your textbook that would provide students additional opportunities for high-level thinking and reasoning?

If we are to meet the challenges and demands of the current tide, we must consider providing our students high-level opportunities to learn that involve opportunities for verbal interaction.   

The next post on this topic will be Anticipating Student Responses and Monitoring Their Work.

More food for thought...

Wow, where did August go?  On the first day of school I suggested that we focus on the Learning Community (LC) rubric of the Teacher Observation Instrument.  Well, how did it go?  I hope you took the opportunity to focus on your classroom practices as it related to building community in your classrooms.  Recall that community is the focus of our PLC Initiative for this school year.  It might be a good time to read the rubric again and reflect on how you see yourself fitting in on the scale. 

So, a new month is upon us this week and it just so happens that another of the rubrics is a natural progression from our last focus: Learner Engagement (LE).  Like the LC rubric, engagement practices are developed over time and refined over time.  Here is the description of the Learning Engagement rubric:

The Learner Engagement rubric is designed to support teachers with establishment of classroom environments that support authentic engagement in learning.  The effective teacher understands the relationship between motivation and engagement and knows how to design learning experiences using strategies that build learner self direction and ownership of learning. The teacher collaborates with learners to develop shared values and expectations for rigorous academic discussions, and individual and group responsibility for quality work. Engagement is both student-to-student and teacher-to-student, and is grounded in development of critical thinking skills focused on content specific process skills. This facilitates authentic engagement where students are not just compliant, but can see a connection between the assigned task and the results/outcomes, and that there is clear meaning and personal relevance.

There are four elements that are used to rate the teacher in LE rubric:

1.       Student-to-Student Interaction

2.       Teacher-to-Student Interaction

3.       Authentic Engagement/Quality of Work

4.       Critical Thinking

All four elements are rated during the actual observation of our teaching. 

Fostering engagement is a practice that takes thought, practice, reflection, and refinement.  I would encourage everyone to be proactive in this endeavor, and help each other grow as professionals practicing our craft.  If you have strategies that you think would benefit this process please make time in PLCs to share so that we can practice building capacity within our department.  Perhaps the easiest of the four elements in this rubric to focus on is the Teacher-to-Student Interaction.  It is somewhat easy to plan for, attempt, reflect upon, be observed by others, and change if necessary.

Remember, the Professional Responsibilities rubric has an element that addresses Collaboration with Colleagues.  As we develop our collective capacity (Teacher Growth, and Relationships are NHS focus areas) building within our department and PLCs we will be growing ourselves in a manner that will allow us to be evaluated at higher levels on the PR rubric.

Have a great September!

PLC Team Leader Training

Today the team leaders attended a half-day session with Dr. Tim Kanold. 

The focus of our day was Formative Assessment Strategies within a sustainable cycle for continuous improvement.

Topics included: 

• Improving the teacher communication and sharing though Blogs-21st Century Communication!  (hence the construction of this blog)
• Improving teacher team communication.
• Reasons why our district cannot break through the barriers of poor performance in math.
• Getting serious about Formative Assessment and student ownership in learning mathematics.

In an effort to improve teacher team communication we were given two tools to use in this effort.  We will be using these tools in our PLCs to assess where we believe we are as a team, and to help improve or efforts in team communication.  The two tools are:  Knowing Your Team History; and Building Communities of Practice.

Dr. Kanold shared with us a brief analysis of our longitudinal CRT data and our D/F ratios.  Among the celebrations were that compared to five years ago we have made great strides in increasing the availability of higher level math classes to students.  The number of students has increased dramatically.  An area that requires some reflection on our part is that our D/F ratio has remained constant over five years.
 
In order to address our concerns with the D/F ratio we are going to focus on grading accuracy in our teams.  Some recommended steps for our teams are:  establish agreed upon rubrics for scoring all exam questions; conduct a group scoring practice session on a sample of student work and responses; and discuss and resolve differences of opinion regarding discrepant scores based on anchor paper agreements.  This is a powerful professional practice.  The discussions with colleagues about the diversity and quality of student work and ensuring greater accuracy in the score a student receives will provide opportunities for equity among our students in their grades.

In addition to accuracy, the question was posed: why do we assess?  Student mistakes on summative assessments such as quizzes and tests are potent learning tools when viewed formatively rather than evaluatively.  The most powerful single modification we can make in our practice that will enhance achievement is specific and timely feedback for student reflection and response.  This should be required by all teachers.

Finally, we spent time looking at strategies for formative assessments.  Work from Wiliam (2011) was cited:  An assessment functions formatively to the extent that evidence about student achievement is elicited, interpreted, and used by teachers, learners, or their peers to make decisions about the next steps in instruction that are likely to be better, or better founded, than the decisions they would have made in absence of that evidence.  The key phrases: evidence about student achievement is elicited and ...makes decisions about next steps are crucial to the process of formative assessment.  The teacher and the students in conjunction with their peers must act on the evidence.  Without action the formative process is empty in terms of impact on student learning.

The cycle of formative assessment for PLCs consists of 5 steps. 

1. PLC Teacher Team designs assessment unit instruments
2. PLC Teachers implement formative assessment classroom strategies
3. PLC Students take action on assessment feedback
4. PLC Teachers use Step 1 instruments for student reflection and action
5. PLC Teacher Teams use assessment feedback to improve instruction

Step 4 is a new area of focus for PUHSD math teams.  Examples of formative assessments and tools will be shared in your PLCs. 

We wrapped up the session excited and ready to attack student achievement in our teams.  Thank you Dr. Kanold for your insights and support.