Reflection on My Reciprocal Observation

Another reflection on a class I conducted which was being observed by an education program classmate as part of my credentialing process.  Not as interesting of a post as others, however, I am using this site to capture my teacher ed program experience as well, for posterity sake, well, at least until I remove certain postings.  Only pseudonyms are used in my postings.


The class embarked upon a new unit effective the day of this reciprocal observation.  The new unit covers parallel and perpendicular lines as well as systems of linear equations.  The lesson plan (Attachment 1) focused on parallel lines.

In preparing for the day’s instruction, I collaborated with my CT about how best to build a warm-up for the lesson.  This discussion led into creating an entire class activity crafted to enable students to explore and discover parallel lines, especially their similarities and differences, before any direct instruction.  The activity also provided an opportunity for students to work on their writing, grammar, and mathematical vocabulary.  I, apparently, was the inspiration for this activity, however, it was my CT, in my opinion, that had the voilà moment while I was thinking out loud about a possible problem for a warm-up and how I wanted to proceed from there; nonetheless, I was very happy with the construction of the activity, and thank my CT for sharing her insights with me so that it could take form.

In accordance with the California Standards for the Teaching Profession (CSTP), (Attachment 2), our lesson plan, and the class activity worksheet itself, touched upon Standard 3: Understand and Organize Subject Matter for Student Learning as well as CSTP Standard 4:  Plan Instruction and Design Learning Experiences for All Students and CSTP Standard 5:  Assess students for learning.

I believe my time in front of the class during this observation, which lasted thirty minutes, was fairly effective; it helped that I used an online countdown timer to manage time in five-minute chunks for each part of the class activity – it worked great.  While there is room for much improvement in my teaching, I am happy with how I: a) handled myself, b) worked with my CT, and c) helped students in their self-discovery process, as required by CSTP Standard 1:  Engage and Support All Students in Learning.  It is still challenging to get a strong sense for individual sense-making on a large-scale, however, I do feel as if I can tell whether the majority of students grasp the content or not by judging students’ responses to questions I ask periodically as well as via whole-class feedback such as “thumbs up, down, or sideways.”  In this case, many students seemed to grasp the concept that parallel lines had the same slope.


What have you learned about your students during this lesson?  What have you leaned about yourself?  What evidence of student learning can you identify, and how does that evidence influence what you will do next?

The lesson started after students finished their end-of-marking-period final exam, which occupied the first twenty minutes of class.  The next thirty minutes were spent walking students through the class activity, which consisted of a worksheet (Attachment 3) where students explored and discovered key aspects of parallel lines, especially their similarities and differences.

During the worksheet activity, I learned more about my students as individuals and as a whole class.  I did so by requesting volunteers for problems and when no one volunteered, calling on students selectively as we progressed in the activity.  The activity initially required graphing four points and the two lines associated with a specific pair of the points, followed by determining the slope of the two lines, finding the equation of each line in slope-intercept form, and, finally, finding the equations in standard form.  Since I normally call on students when leading warm-ups or homework reviews, they seemed to take in stride my calling on them as part of the class activity.  Even one of the lower performing students, with a D for the second marking period, volunteered to give her solutions for the slope of both lines, which was pleasantly pleasing; albeit she solved it by counting the change in y (rise) and the change in x (run) computing the ratio of rise/run.  She nonetheless, made a huge leap forward in class participation since she normally hides out, texting and chatting with her group mates.  After she finished, I took the opportunity to express the general formula for computing the slope of a line between two points, which most of the class already knew since we covered it extensively in the earlier unit.  Another student, with a C- for the marking period, worked a problem to find the equation of a line at the SMART board, solving for the slope even though it had been found in a prior step, which he apparently did not recall or connect to the current problem.  Regardless, he correctly determined the equation of the line in proper form, and learned from my comment that the slope had already been computed so he simply needed to carry it forward into the current problem and substitute it for “m,” the slope of the line in the equation y=mx+b.  Finally, for determining the equation of the same lines in standard form, Ax+By=C, my CT suggested, for the sake of time, that I show the class how to do the first of the pair of problems, then call on a volunteer for the last of the pair, which went well.

Prior to, and during, this lesson, I learned that I could improve my planning and teaching capabilities by collaborating with my CT.  My ideas sparked those in her and vice versa.  It was a wonderful experience and one I hope to keep up going forward with her, in spite of the occasional flare-ups in our communications, which primarily are due to misunderstandings on both sides.  However, with time to reflect, we get back together to discuss what happened, how it might be done differently next time, or some other idea on how to improve our working together and collaborating.  We are both committed to working together in a professionally beneficial way so that we both benefit from the experience.

All in all, my experience taught me I have much to learn as I progress as a student teacher.  I am fortunate to have the opportunity to work with a CT who supports my learning.  I look forward to what each day may bring to me, and I to it, as I seek to develop the skills of an effective teacher.  While some days are challenging, sometimes incredibly so due to the emotions accompanying misunderstanding another human being, or dealing with dozens of students, it is exactly what I hoped for in terms of serving a community of students who struggle with learning, but deep inside have much, if not all, of what it takes to succeed, it’s simply having someone point it out and help activate it in them.

About Dave aka Mr. Math Teacher

Independent consultant and junior college adjunct instructor. Former secondary math teacher who taught math intervention, algebra 1, geometry, accelerated algebra 2, precalculus, honors precalculus, AP Calculus AB, and AP Statistics. Prior to teaching, I spent 25 years in high tech in engineering, marketing, sales and business development roles in the satellite communications, GPS, semiconductor, and wireless industries. I am awed by the potential in our nation's youth and I hope to instill in them the passion to improve our world at local, state, national, and global levels.
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