Activity Two:  Discussing the Discussion

I was really hoping for something spicy to be said on the discussion board!  Seems we are all pretty amiable folks in education; so wanting to do the right thing for our students that we will try anything!  And the result of this is a lovely balance between the old and the new – which feels right.  

Remember the push for whole language reading?  And how we swung back to phonics after we recognized that students really do need to foundational patterns on which to build more sophisticated thinking and skills?  Compellingly, these trends in math seem to go the same way. 

What is telling is that the debate, though critical, seems to be contained primarily to those in education.  I remember the whole language debate on the 6:00 news, with everyone and their third cousin weighing in.  The public seems suspiciously quiet though this continuing struggle in mathematics education.  I suspect that this relates back to the idea discussed at length on our discussion board about attitude toward mathematics.    Much of the public feels uncomfortable with maths, and throw their hands up in frustration at the idea of discussing something so utterly un-understandable.

Of all the potentially controversial discussion points presented on our board, the question that has stuck with me is that of accelerating the curriculum.  How does this work for students?  And isn’t a fluid approach to skill learning embedded in problem-based learning?  And what does that mean for the baseline understanding of mathematics needed by classroom teachers?  As competency needs increase, how does that affect teacher training and continuing education?

MLB 1 What is Math?

29 x 12 = The Big Question

I solved 29 x 12 = using the standard algorithm, following the steps I teach my students.  First, I estimated the answer by rounding the multiplicand and multiplier to the nearest ten: 30 x 10 = 300.  I know my answer will be higher than 300, by about 30.  Then, I set up the algorithm vertically and began multiplying the numbers in the units column.  I ended up with 29 x 12 = 348, which is appropriately close to my estimated answer.

For a fleeting moment, I thought about solving it in my head, by cutting up the numbers into 30 x12 and 9 x12, but that felt like a lot of brain power on a Friday night, when using the algorithm is quite efficient for me. 

The TERC video featuring 5th grade students explaining their solutions to the same problem demonstrated impressive logical thinking and articulate explanations.    The first student explained that he split his multiplicand into 20 and 9 and multiplied them separately by 12. He then added those two products together for his final answer. He described the 20 as 2-10s, and easier with which to work.   To check his work, he did repeated addition of 29, 12 times and found the same answer: 348.  One of his classmates noticed that his work paper showed additional work, involving a 90, and asked for clarification.  The student explained that he had also split the multiplier in two numbers, 10 and 2, before multiplying them by 9.

The second student shared a different approach to solving 29 x 12.  She used repeated addition as her beginning strategy.  However, she read that she rounded the 29 to 30 for use in the problem, because 30 was an easier number with which to work.   After adding 30, 12 times, her answer was 360.  She then subtracted 12 from t360, representing the 12 extra 1's that were added by using a rounded number, instead of the original 29. 360 - 12 = 348.  When the teacher asked for clarification about using 30s, instead of 29's, a classmate explained her process of substituting 30 for 29 and subtracting the "extra" 12 for accuracy.  

When watching the TERC video the second time,  I noticed the authentic understanding of the students that became clear when they were asked by their peers to clarify their thinking or restate a strategy used by a classmate.   When reflecting and explaining their mathematical thinking "off-script" one could see that the understanding was genuine.  The first student was able to use two strategies to solve the problem - the first illustrating conceptual understanding (splitting the numbers into smaller parts) and the second expressing a more efficient means of calculating the answer (checking with the standard algorithm)   Both the presenters and the listeners engaged fully in the activity.  

The role we saw the teacher perform was that of facilitator - disguised as curious on-looker - directing the students to explore and explain their thinking through exploratory questioning.  This role allowed the teacher an opportunity to see the depth of student understanding and engagement, as well as see misconceptions a student may have created.   Though we did not see any examples of this in the short video, such mathematical conversations among students and teachers allow both to see misconceptions and provide an opportunity for reframing ideas, or a-ha! moments, through the sharing and explaining process.   Assessing and teaching in one seamless activity (if the stars are aligned correctly, anyhow.)

Mathematics is the discovery and use of patterns to make sense of the world.  Mathematical thinking involves the process of looking for and recognizing these patterns and applying them to life.  That translates into a different kind of maths in the classroom - one where students are completely engaged in their thinking.   These engaged students create their own understanding of mathematical concepts based on experience and experimentation.  This requires patience and facilitation (and behavior management!) skills on the part of the teacher, and persistence and risk-taking on part of the students.    

Getting to Know You!

The teacher with whom I spoke is a veteran of teaching - over 15 years of loving and learning - and is a devout life-long learner.  In truth, I chose Ann because she and I hold many of the same beliefs and I was curious to see just how deeply our professional ideals bound.  I was thrilled to discover her endless ideas and openness to collaboration and coaching. 

One thing I appreciated was that with her experience came a willingness to explore how to be a better facilitator of learning.  She was not threatened or overwhelmed by the coaching process in the way that two of my other colleagues were.  I suspect that this is because she is secure enough in her fundamental competence to be able to make changes or adjustments in thought without having to throw away hours of work in planning.  I was reminded of the Phases of Beginning Teacher's First Year diagram from Bay-Williams, McGatha, et all (2014), where disillusion and exhaustion dominate the middle part of the school year and one struggles to stay afloat, much less take on new ideas.  My two less experiences colleagues really liked the idea of such work, but felt overwhelmed by the time and emotional energy it would take.  I totally sympathize! 

The most inexperienced teacher at our school has 6 years teaching experience.  Lucky for me, just least year she moved from first grade to fifth grade and feels all the jitters and uncertainty and thrill of facing a new challenge - much as a new teacher would.  Additionally, she is a very structured and anxious person for whom working with new content holds a high degree of stress.

Talking with Elizabeth reminds me that working with new teachers will require a different process, beginning with asking the question, "How can I help you right now?" and being willing to do whatever that might be at that point in her process.  This may mean helping her set up a realistic way to handle grading demands or collecting resources for an low functioning student, instead of discussing how her students reason abstractly and quantitatively.  I also believe that new teachers can be more reflective (and self-critical) than more experienced teachers, which can result in fabulous opportunities for growth and professional satisfaction.  Our strengths are abound!

Intention is the key word today:  Teaching with intention.  Listening with intention.  Learning with intention.  Writing with intention.

Reading through the Shifts in Classroom Practice the first round,  my immediate emotion was despair.  (Well, that word might be a little strong.)  As a school, we are not very far along on the continuium in any of the seven categories.  

However, I do see solid work in improving Shift 7 and Shift 2.  Though much of our instruction is still quite teacher directed, each class spends part of each double lesson on problem solving in small groups.  Our strength in these shifts are: (1)  designating time to those experiences and (2) recognizing that student discussions can be rich with processes and content learning.  Unilaterally we struggle with differentiating within the classes - primarily getting students with lower skill levels to engage. 

Part of this challenge is that national law does not allow for groupings based on perceived ability (it is against the law to group children by ability and thereby offer them challenges appropriate for their level of understanding.  Though we all try to work around this when possible.)  And part is our lack of knowledge about appropriate questioning and how to point struggling groups in the right direction, while allowing for discovery and ownership.  These obstacles are surmountable, though, and we continue to work towards becoming a community of learners.

As a teacher leader, I recognize what a strength we have in being a school that participates in Lesson Studies.  The Lesson Study structure allows us to explore ideas or concepts in Leading for Mathematics Proficiency framework within an established set of guidelines.  Through this, I am able to support my colleagues by (1) providing information about the Shift focus in the form of handouts, articles, and presentations; (2) help formulate a question and goal associated with our Shift; and (3) participate in planning, data collection, and processing of information with the whole group. 

Reflections on the Coaching Cycle:

I laughed out loud ( in glee)  at Steven Covey's work being sited as a resource in a math learning textbook.  

I was also intrigued that so much of the space and energy given in the Coaching Cycle is devoted to building relationships.  I wonder if such emphasis is specific to helping fields - teaching, nursing, psychology, social work, ministry - or if that is necessary because some teachers are not initially open the coaching experience.  Having another adult in the classroom can be unsettling; our carefully created dens invaded by another momma bear.  Bay-Williams, McGatha, et al (2014)  wrote about relabeling the three-stage process from pre-observation, observation, and post-observation to more collaborative ideas, less threatening words: planning, data gathering, and reflecting.   Given this emphasis on relationship building, I was drawn to three concepts presented:  trust, rapport, and questioning.

Trust:  Our school is starting our second year of Lesson Study cycles.  The growth we have felt as a collaborative team is monumental.  One of the key elements of that process for us has been building trust.  Teaching teams at our school are small, with one teacher at each grade level and subject teachers who rotate around classes.

Two years ago, the school reorganized, and the people - and dynamic - with whom we worked changed dramatically.  The result was a year of negotiation and compromise, where we often left meetings upset.

Through the process of  Lesson Study, we  began identifying what we appreciate about one another and took steps towards becoming an open teaching community, rather than individuals behind closed doors.  Understanding that without judgement, we could nurture one another professionally.

Building Rapport - I am really interested in trying In my past life, I worked as a clinical social worker, where rapport was paramount to problem solving with my clients.  McGatha, et al (2014)  presented mirror neurons as the pathway to building rapport with others.   I considered the actions I purposely use when talking with people - eye contact, nodding, changing facial expression, mindful listening.  I had not really considered mirroring posture or gesturing as part of relating to others.   I remember talking with a very challenging parent over and over 15 years ago.  We had many meetings, most of which were contentious.  It gave me lots of practice being aware of - and try to control - my body during difficult situations.  It was really difficult to have an open body when I felt attacked, even when I was conciously moving myself it an open position.  This idea I will begin observing immediately.

Questioning: This area challenged my thinking.  I believe entirely in the power of questioning to increase learning.  I also struggle to know how to question and to take the time in the planning stages of a lesson to prepare questions that improve learning.  This is an area in which I hope to see the most personal growth over the course of this next term.

In regards to questioning, Vignette 3, which illustrated off-topic inquisitive questioning,  felt tremendously real to me.  I recognize that urge to