Cognitive Coaching to Student Success

Speaker began by listing his credentials: undergrad @ Aquinas, grad @ GVSU, HS/MS english teacher, then MS assistant principal and then elementary principal.  Presented data from Tri County district showing growth of students in MEAP and pre-ACT (8th grade) growth over 2011-2014.  His argument for such growth comes from administration and teachers being cognitive coaches.

Definition of cognitive coaching- to produce a self-directed person with the cognitive capacity for self-directed acquisition of knowledge.

Key tools that teachers need to use to be the best cognitive teachers include:

Conversation techniques: planning, reflective, identifying problems/solutions, and gathering data on effectiveness of conversations.  Then teachers must have specific mental mindsets everyday to be cognitive coaches; efficacy, consciousness, independence, craftsmanship, and flexibility.  In essence, a cognitive coach believes that all answers lie within the student, and it is the teacher’s job to employ a proper mindset with good questioning skills to really draw out the new thoughts/ correct thoughts from their students.

There exist four supporting functions that coaches do: coaching conversations i.e. “teacher mode”, collaborating- one-on-one students in class, consulting- not something we want to do until the student is basically saying “IDK”, then coaches need to properly/effectively/fairly evaluate both how their students have done with the material, and how you, the teacher/coach has done in presenting the material.

So principals (assistant) serve as teacher cognitive coaches; thus, a.p.’s fulfill the role that checks on the teacher to help the teacher best plan out, execute, and then evaluate an entire unit.  Simultaneously, a teacher serves as their student’s cognitive coach by employing the aforementioned conversational tools to maximize student potential.

Hence a “procedure” for being a cognitive coach both as an administrator and as a teacher is to utilize lots of questions to draw out all of the questionee’s knowledge, and then ask their permission before giving advice/right answer.  This grants respect from the coach to the coachee that is vital to encourage both between administration and teachers, but more importantly, between teachers and students.  So the goal of a coaching session is to get the coach thinking on the same ‘wavelength’ as the teacher/student.

Cognitive coaching as a teacher is a great way to get both formal and informal formative assessments done because each session allows the coach/teacher to get a gauge of how much knowledge the student has.

When teachers are being coached, then the session is about getting their thoughts organized and getting a good feeling  (as an administrator) of how well the lesson seemed to go, and any pros/cons/changes that the teacher noticed pre/post lesson.

He then presented what administrators should focus on during monthly staff meetings- use them as time to better themselves as instructional leaders!!

Discussion of a Lab Classroom cycle in which a host teacher has a coach (administrator from different district) and guest teachers observe a pre-lesson interview between host and coach, observe lesson, then a post-lesson reflective session.  Guests look for all sorts of things including: student comprehension of lesson, issues presented/came up in lesson and how teacher dealt with them, and in pre/post lesson their thinking/emotions/expectations/feelings on the lesson.

Wrapped up with handout Scanned from a Xerox Multifunction Device Device by Jim Knight on cognitive coaching and a spiel on formative assessment:

snowball, thumbs up/down/side, exit slip, etc.

Adaptive schooling is a focus on differentiating between a discussion and a dialogue.  Essentially one directional vs. two directional communication.

Overall, this is what I think of this set up for teachers.  For new/incoming/rookie teachers [defined as less than approximately 5 years experience], this is great because it gives them a new support to bounce ideas off of and a different environment in which they can organize their thoughts and ask questions about their ideas. The only thing I would be concerned about is that my personal preference is that when I ask a question, I expect an answer, not a series of questions designed to make me discover the answer.  Now I realize that I am splitting hairs a bit because that type of questioning is extremely valuable for teachers to use with students, and it can be helpful in this context of having a cognitive coach; however, at a certain point in time, I need to get a straight answer.  Most likely, that would be only a minor thing to be concerned about.

For older/veteran teachers, this set up could go either way depending on how flexible/inflexible they are.  The simplest way to explain this is to consider the old mantra: “no one likes change”.  From there, we can see that those who have been doing things their way for a certain amount of time and then they are told to change it all could result in a disastrous outcome.  That being said, I am confident that those “good” teachers would recognize the benefits of having a cognitive coach.  Then they would augment their approach to teaching accordingly.

As a future teacher, I would really like to have a cognitive coach available to me in my first teaching job because the knowledge of having that extra support goes a long way; plus the coach will be a great source of ideas/advice for how to proceed with a particular unit/lesson.

Presenter: (Steve Johnson)


Blog post 3: Instrumental vs. Relational Understanding

Recently, we, in MTH 329-01, began our unit on proportions and fractions, and a related article is the following one by Skemp.

This is a phenomenal article in which the author makes a strong case as to why all instructors need to begin teaching mathematics, and all subjects, in a relational manner.  His biggest supporting point is the fact that research in related educational subjects reveals that when students are taught relationally, their long term cognitive abilities in that subject are drastically superior to students who were taught the same subject in an instrumental fashion.  Furthermore, Skemp gives four reasons as to why relational teaching (aside from the primary mentioned above) is drastically superior to instrumental:

1. The means become independent of particular ends to be reached thereby.
2. Building up a schema within a given area of  knowledge becomes an intrinsically satisfying  goal in itself.
3. The more complete a pupil’s schema, the greater  his feeling of confidence in his own ability to find new ways of ‘getting there’ without outside help.
4. But a schema is never complete. As our schemas enlarge, so our awareness of possibilities is there-by enlarged. Thus the process often becomes self-continuing, and (by virtue of 3) self-rewarding. (Skemp 8).

Clearly these are all goals that we, as future math educators, want to encourage and see develop in all of our students; however, as Skemp points out with his last section titled “Theoretical Formulation”, these ideals only hold weight in an abstract or experimental situation/classroom, and NOT in actual USA classrooms.  Obviously this is a disappointment, but it is also not the least bit surprising.  This is because Skemp gave four points as to why instructors choose to teach instrumentally.  They are:

1. That relational understanding would take too long to achieve, and to be able to use a particular technique is all that these pupils are likely to need.
2. That relational understanding of a particular topic is too difficult, but the pupils still need it for examination reasons.
3. That a skill is needed for use in another subject (e.g. science) before it can be understood relationally with the schemas presently available to the pupils.
4. That he is a junior teacher in a school where all the other mathematics teaching is instrumental. (Skemp 6).

Skemp also gives some reasons as to why a curriculum or outside forces also push instructors into an instrumental teaching method:

1. The backwash effect of examinations.

2. Over-burdened syllabi.

3. Difficulty of assessment of whether a person understands relationally or instrumentally.

4. The great psychological difficulty for teachers of accommodating (re-structuring) their existing and longstanding schemas, even for the minority who know they need to, want to do so, and have time for study. (Skemp 6).

I would just like to point out that the rise and dominance of ACT, SAT, GRE, Common Core, and the like all dramatically increase the impossibility that any teacher, but especially new teachers, have a chance to even attempt instructing relationally due to the high demands of all the standardized tests and regulated curriculum.  That being said, Professor John Golden told us that the most important thing we can do as teachers is to make the best choices for our students within the realm of things that we, as teachers, can control.  Example being that if our district demands the “butterfly method” be taught to 5th-6th graders, then we as teachers should discover relational links between butterfly method and other fractional topics, thus ensuring or at least increasing [hopefully!!] the understanding of the covered mathematical topics.

Furthermore, I believe that all of Skemp’s reasons as to why teachers forgo relational instruction can be summed up as follows: instrumental is significantly easier and more time efficient to teach to students than instrumental; hence, since USA school curriculums become increasing “big test” oriented, instrumental becomes more and more attractive to all teachers, NOT just new ones.  Additionally, Skemp’s 2nd points in both outside factors and primary factors directly relate to each other, and combined, they create a vicious cycle that creates a never ending need for more and more stuff in a more condensed time frame for standardized tests; thus, leaving only one option available to teachers whom want to cover all relevant material and (due to common core and higher review standards) keep our jobs.  Finally, consider all of Skemp’s arguments for relational.  Upon simple examination, it is apparent that all four look/sound like fantastic goals for teachers to have, but with closer inspection, we notice that a significant amount of effort might/can/will be needed to develop this in every student {approximately 30 per 3-6 classes} equates to 120 or so students that all learn in varied ways.  It follows that, in only an 8ish hour day, that a teacher gets maybe 1 hour per class to “teach”, but that leaves a very small amount of time [even if all 60 min/class is spent in group/one-one discussion] it seems nearly physically impossible to achieve such a lofty goal given current resources/demands on single teachers in USA classrooms.

Personally, I feel that we {as [future] instructors} should endeavor to teach relationally all mathematical content to every single student that enters our classroom for the simple reason that it is our job to not only learn mathematics, but to obtain skills vital to survival and prosperity in a democratic society.  This is perfectly aligned with Skemp’s reasons to teach relationally because, in USA, we tend to value individualism/uniqueness, innovative, confidence, independence, and creativity.  These traits are directly developed and supported from all four of Skemp’s justifications to teach relationally.  This is because a student who internalizes their desire to learn mathematics (and other academic topics) shows a drive to better themselves, and when they discover several different techniques to solving similar problems, this will have built up their creativity and innovative skills.  Also, their skills will grow and the student will no longer need to be scaffolded in mathematics; thus increasing their confidence in both mathematics, and in life in general because mathematics is touted as “hard”, so when the student gains a powerful grasp of mathematics, then they feel emboldened to try other challenging things that may or may not deal with mathematics.

Overall, I really enjoyed reading this article and grasping/processing what the article is saying and how it will impact my teaching methods/choices when I am in the classroom.  That being said, I feel it will be best to try and emulate what Skemp wants, but, until something changes, do not sacrifice material that is on ACT, SAT, etc. in loo of improving relational knowledge on fewer topics i.e. balance between quality and quantity must be maintained, but quantity, in this situation, beats quality.

P.S. We also played a game called “bizz-buzz”, which is an, allegedly, drinking game, which has been adapted to counting fractions and recognizing equivalent fractions.  I found the game fun.  Not much else to say on this.

Thanks for taking a few of your precious minutes to read this.  I hope that you found this useful/interesting.

2nd Blog

Alright, so we are now into the start of February, and I have some new thoughts about proportions.  First I have just finished reading the Billings article on proportional reasoning, and i found it fascinating.  This is due to the fact that she recommends using a “no numbers first” approach to introducing proportions to middle school students.  Her argument for this is that this allows instructors to better understand where their students are in terms of their initial proportional reasoning skills.  Thus this is an excellent way to both administer a diagnostic assessment to gather useful data on our students, but also to use as a formative assessment(s) to gauge how well our students are grasping the concept.

Furthermore, she argues against teaching, initially, the cross multiplication strategy/algorithm used to commonly solve proportional problems.  The basis of this follows from the fact that students will then simply memorize the procedure for dealing with proportions, without necessarily comprehending the logical reasoning behind why proportions work the way they do.

Also, we did an in class activity on Day 7 (1-28-15) in which I had the opportunity to “play teacher” to the class.  For this activity, we were tasked with identifying, in a series of 7 problems, which set of solutions had more “blueness” too them.  What I had to do was illicit student responses and get them to explain their reasoning behind which answer they believed to be right in a ‘pure’ mathematical sense.  Overall, the activity was fun, but as I explained on my thoughts about that day’s activity, I felt like it is difficult to simultaneously divorce your own experience and knowledge from the problem and keep and open mind when dealing with an actual class of middle school students who do not really have a firm grasp on what proportions are.  Hence my solution to clear up some confusion is to be explicit in my questions on formal and informal assessments as to whether or not I am looking for a proportion or an actual integer or something else.  That being said, a good bonus question or formative assessment would be to investigate whether our students can correctly identify which contexts require proportional reasoning compared to integer or other kinds of reasoning abilities.

Thanks for taking a few minutes to read my thoughts on proportions and teaching the topic.  Hope something is useful/thought provoking.