List of Contents

Summer 2017

Editorial

Section: Teaching Practice and Action Research

Rethinking Instruction of the Tangent Line of a Circle
Jae Ki Lee, Susan Licwinko, Borough of Manhattan Community College

Active Learning in Developmental Classes of Mathematics
Malgorzata Marciniak, LaGuardia Community College

Section: Teaching-Research

Assessment of the Depth of Knowledge (DoK) Acquired During the Aha!Moment Insight
Bronislaw Czarnocha, William Baker, Hostos Community College

Appendix. Collection of Aha!Moments collected during the Teaching-Experiment

Section: Notes from the field

Minutes from the Meeting with a Student-Researcher
Malgorzata Marciniak, LaGuardia Community College

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Editorial

The Summer ’17 issue of MTRJ brings reports from Community Colleges of CUNY, from BMCC, LCC,HCC. In the future issues of MTRJ, we are planning to focus on the faculty of CUNY’s community colleges as a very unique faculty amongst the professors of community colleges nationwide. Only approximately 8-14 % of college faculty have PhD degrees in their disciplines as accordingly to AMATYC, MA or MS degrees are sufficient for the job. However ourselves, cc faculty of CUNY, in the majority we have PhD’s in our disciplines, hence we know what is research, the research skills and methods. On the other hand, addressing myself to mathematics faculty, we also have a very deep knowledge of teaching elementary, high school and college, courses of mathematics. Together, when integrated and synthesized can create a powerful, creative method of doing research on learning while teaching that each of us can develop. Together we can create a new and unique domain of knowledge and practice based on our unique experience Teaching-Research.

We present two Action Research investigations of familiar to all of us issues, construction of the tangent to the circle and the active learning.

Jae Ki Lee and Susan Licwinko from BMCC point our attention towards two different methods to obtain the equation of the tangent to the circle from a distant point, through implicit differentiation and through geometric construction. They report students’ appreciation for the geometric method as much simpler.

Malgorzata Marciniak from LCC discusses her approach to learning based on the worksheets, which include corrections made on the basis of student comments and efforts. She is discovering the role of classroom iterations of the intervention with the refinements in between – the basic unit of teaching-research focused on the improvement of learning. She also is discovering common problem for our students that is absence of attention to connections between different examples, different concepts.

Teaching-Research
Broni Czarnocha from HCC presents the results of the pilot teaching-experiment focused on facilitation and assessment of the Depth of Knowledge reached of Aha!Moments in mathematics classroom as the beginning of the formulation of Aha! Pedagogy. The work will be presented at the Conference of Teaching Research for All Students (CTRAS 9) in Dalian, China. He points out that the standard tools of assessing Depth of Knowledge on the basis of instruments derived from Bloom’s taxonomy are essentially insufficient in their static descriptions of the levels. We need the ability to assess “pre” and “post” knowledge reached during the insight; it involves “jumping” between different levels rather than reaching one particular level. An interesting component of his teaching experiment was the participation of student-researchers, who together with the author participated in the facilitation process of Aha!Moments as peer mentors in the classroom. Work with student-researchers connects his work with the Notes from the Field, where Malgorzata Marciniak presents notes from her Teaching-Research diary on starting the work with student-researcher in ideals of commutative algebras. The surge in the student-researcher concept present interesting and challenging idea in terms of close TR investigations concerning the process of learning in this environment.