Rules of Exponents and Fractions are Student's Nemesis in Calculus!

Submitted by Becky Baranowski on
What is the Purpose of the Assessment?

In my calculus I class, 50%-75% of my students do not do well on one particular integration problem that requires basic rules of exponents and fraction knowledge.   

Describe the necessity for this assessment

The need is due to having high failure on this problem which utilizes foundational math concepts students should know before entering MAT22X.  

Describe how the practice will be implemented

For 10 years, I have implemented several things to address this ONE problem - Review prior knowledge at the beginning of semester; drill and kill during class; collect homework specific to the problem; group work; board work; daily quizzes; journaling; telling them flat out that this problem will be on the exam; Khan Academy; review throughout the semester; detailed feedback; a mix of all of these, etc.    

Interpret, compare, and describe the results

I see no pattern of anything truly helping.  This semester, I still had 19 of 30 students not be able to do simple algebra in a calculus class.  I am at a loss.  They did well on the "harder" integration problems, so why can't they do algebraic integration?  This semester, I incorporated so many different techniques with students in hopes of them doing well.  I think this goes back to the core concept students struggle with - fractions. 

After analyzing, and reflecting on the outcome, what are the next steps?

Clear communication and collaboration between faculty is so important to make sure our curriculum lines up throughout the sequence of math courses.  WIth developmental education gone, faculty teaching college level classes will need to incorporate review of basic concepts within their courses.  Open dialogue and collaboration with instructors are always important.  We need to make sure our courses are in alignment with each other.  


Please note:  From speaking with faculty in the prerequisite coureses, they are incorporating reviews of rules of exponents and fractions.  But, at what detail and how, I am unsure.  Hopefully with the creation of SLOs and having Guided Pathways, we can come up with some activities and best practices as a group to help students understand these two concepts better.  I am not happy with the idea of just accepting that students will not be able to integrate a fractional problem that requires rules of exponents.  There has to be something out there to help our students be successful with this.  See attached for a sample problem that I am refering to.  

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Teri Graham Mon, 04/15/2019 - 10:35am

Becky - Thank you for sharing your experiences.  Now that the district has removed our developmental math path, I am concerned that this experience will increase for you.  Unfortunately, I think there are many pieces of pie that lead to the cause/effect of this dilemna.  Learning that high schools no longer require homework, I see more and more of my students simply don't practice outside of the classroom.  I am concerned that an integrated "quick review" in a 16 week college course (that I would normally spend weeks on in 08x, makes it difficult to heal 12 years of academic habits, fears and beliefs of our students.  You are seeing the ripple affect.... 

Becky Baranowski Wed, 04/17/2019 - 6:25pm

In reply to by Teri Graham

Thanks for taking time to comment.  I completely agree that I am seeing the ripple effect.  Thank you for doing what you can in your courses.  Having communication with you has greatly helped students who come from your classes and enter into calculus.  I have always appreciated our collaborations to help our students transition from dev ed to science and calculus courses.  

Rachel Smith Wed, 04/17/2019 - 1:48pm

I love this CATS.  It's simple and to the point.  And it completely reflects my experiences with many parts of BIO181.  After 15 years of trying many different approaches, there are still things that students regularly struggle with and none of the interventions seem to move the needle.  It illustrates that sometimes there are NO curricular interventions that are the magic silver bullet.  It's down to student preparedness and student behaviour, much of which is outside of our control.   

I have noticed that as I am "maturing" (hahahaa) into being a "veteran" instructor (LOL) I am becoming less interested in modifying my content pedagogy (since it doesn't seem to help shift the needle) and more interested in the things I can do to influence student behaviour, attitude, engagement etc....      as that is possibly where we can make a difference....