DSCC | Calculus Intensive | Lu Bin | Function of Real Variable | CLO • Assessment • Alignment

Math 130 B: Function of Real Variable | CLO, Alignment, Assessment 

Align the course learning outcomes with course assessment. The steps I took were that I first revisited the CLO of the course, made revisions by considering cognitive level, and action verbs from the ACUE course. Then revised and updated questions for assessment. Typically, real analysis (major core) classes are extremely challenge for our students, seeking any innovative pedagogy and being flexible to adopt effective pedagogy are helpful for students’ learning.

Problem 1 (before): Suppose that $f:\left(a,b\right)\longrightarrow\mathbb{R}$  is differentiable, with  $\left|f^{\prime}(x\right)\left|\le M\right|$for all $x\in\left(a,b\right)$and some $M>0$ . Prove that $\lim_{x\longrightarrow a^+}f\left(x\right)$ exists.

Problem 1 (Revised) 

1. State the definition of a function $f: (a,b)\to \mathbb{R}$ being uniformly continuous on $(a,b)$.
2. State the definition of Cauchy Sequence.
3. Assume that $f: (a,b)\longrightarrow \mathbb{R}$ $\lbrace x_n\rbrace\subseteq (a,b)$ is uniformly continuous, and $\{x_n\}\subset (a,b)$ is a Cauchy sequence. Prove that $\{ f(x_n)\}$ is a Cauchy sequence.
4. Suppose that is differentiable, with $|f'(x)|\le M,$ for all $x\in (a,b)$and some $M>0$ . Prove $f$ is uniformly continuous on $(a,b)$ .
5. Suppose that is differentiable, with $|f'(x)|\le M$  for all $x\in (a,b)$ and some $M>0$. Prove that $\lim_{x\to a^+} f(x)$

 exists.

Implementing this practice made my revisit the learning outcomes for the course, and redesign  and update the course learning outcomes by the well known backward design. With updated and revised learning outcomes, assessment questions can be revised and aligned, with the learning goals are clearly stated and highlighted. Using this new approach, students are more motivated and engaging learning. Compared with assessment questions, students performed much better with the updated questions (aligned with the CLO).

Within group of the same subject, the discussions are more related to ourselves

One take away from the our owe “observe and Analyze Session” with colleagues was that it is reconfirmed what was learned: be more flexible in adopting teaching pedagogy.

 

Evidence of Instructional Change

Assessment Report I	Assessment Report II	Acue Badge earned

 

Changes in Course Syllabus and Schedules:

Pre FLC - Syllabus and Schedule Download Syllabus and Schedule

Post FLC - Syllabus and Schedule Download Syllabus and Schedule

 

Faculty Bio

	I am a professor in the Department of Mathematics and Statistics. I joined the department in 2003,  after working at the University of Arizona as a postdoc fellow for three years. Besides my math interests, I am also interested in innovative pedagogy in teaching.

 

Program Sponsors

	This work was supported by: National Science Foundation Hispanic Serving Institution Project STEM Zone DUE 1832335 US Department of Education Hispanic Serving Institution Project Degree with a Purpose P031S210061 US Department of Education Hispanic Serving Institution Project STEM4Equity P031C210012 *Any opinions, findings, conclusions, or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation or the US Department of Education.