Expert Tips for Tutoring Algebra: Avoiding Common Mistakes

  • Thread starter Thread starter harvellt
  • Start date Start date
  • Tags Tags
    Algebra Tutoring
AI Thread Summary
The discussion centers on helping college algebra students who struggle with the concept of manipulating equations, particularly the misconception of "moving" terms from one side to another. This misunderstanding leads to frequent sign errors and complications with radicals. It is suggested that a solid grasp of fundamental properties of real numbers, equality, and operations is essential for these students. Reteaching concepts such as the commutative and associative properties, distribution, and the laws of exponents is recommended. Emphasizing the importance of performing the same operation on both sides of the equation, rather than "moving" terms, can clarify the process. Using examples to illustrate this method, such as isolating a variable through inverse operations, can reinforce understanding and reduce mistakes. Overall, a focus on foundational skills and clear examples is key to improving their algebraic proficiency.
harvellt
Messages
95
Reaction score
0
Im not a math master yet. I'm a physics major in calc. 3 at the moment and I am trying to help a couple friends in college algebra. They both have this conceptual problem of thinking they are "moving" stuff from one side of the equation. It is causing tons of sign mistakes and causing a lot of trouble with radicals and such.
Does anyone have some good examples that show your just doing the same thing to both sides of the equation, or is the best way to do a lot of examples and make the "show all their work'?
Thanks!
 
Physics news on Phys.org
Your friends in College Algebra studied and should have mastered some important properties of Real Numbers and properties of equality and of inequality part-way into their study of Intermediate Algebra; even possibly before they finished Introductory Algebra. Spend time reteaching your friends the commutative and associative properties for addition and multiplication, the distribution property, the identity properties, and the ...can not remember what you call them... properties of equality and inequality. Also substitution principle. They need to know the properties and to have acquired the associated skills, so maybe you can just reteach them to your friends. You might also give a review of laws of exponents. Pick any book you like to use for teaching (reteaching) these ideas and skills.

Really, if these College Algebra students are having the trouble as you have described, the earned prerequisites for the course are dubious. (Maybe "dubious" is the wrong choice of word.)
 
Of course you are really doing the same thing to both sides. But a short cut is to cancel the operation and do the opposite operation to the other side. This always gives you the right sign and takes less thought and time.
 
harvellt said:
Im not a math master yet. I'm a physics major in calc. 3 at the moment and I am trying to help a couple friends in college algebra. They both have this conceptual problem of thinking they are "moving" stuff from one side of the equation. It is causing tons of sign mistakes and causing a lot of trouble with radicals and such.
Does anyone have some good examples that show your just doing the same thing to both sides of the equation, or is the best way to do a lot of examples and make the "show all their work'?
Thanks!

If that's the case then don't "move" stuff from one side to the other.

Do the inverse operation to BOTH sides.

say x+2=4
x+2-2=4-2 because you are trying to ISOLATE x by itself
which leaves you with x=2
 

Thread 'What are the best A-Level options for someone wanting to do Physics?'

Bit Britain-specific but I was wondering, what's the best path to take for A-Levels out of the following (I know Y10 seems a bit early to be thinking about A-levels, but my choice will impact what I do this year/ in y11) I (almost) definitely want to do physics at University - so keep that in mind... The subjects that I'm almost definitely going to take are Maths, Further Maths and Physics, and I'm taking a fast track programme which means that I'll be taking AS computer science at the end...
View full post »

Thread 'Hepth programs in Europe'

After a year of thought, I decided to adjust my ratio for applying the US/EU(+UK) schools. I mostly focused on the US schools before, but things are getting complex and I found out that Europe is also a good place to study. I found some institutes that have professors with similar interests. But gaining the information is much harder than US schools (like you have to contact professors in advance etc). For your information, I have B.S. in engineering (low GPA: 3.2/4.0) in Asia - one SCI...
View full post »

Thread 'Should I pursue a masters degree after 4.5 years working in IT?'

I graduated with a BSc in Physics in 2020. Since there were limited opportunities in my country (mostly teaching), I decided to improve my programming skills and began working in IT, first as a software engineer and later as a quality assurance engineer, where I’ve now spent about 3 years. While this career path has provided financial stability, I’ve realized that my excitement and passion aren’t really there, unlike what I felt when studying or doing research in physics. Working in IT...
View full post »

Similar threads

I How do Tensors "work" in relation to linear algebraic objects?
Replies
7
Views
264
Tips for Tutoring Math: From College Algebra to Differential Equations
Replies
4
Views
5K
Studying I have some epic math goals and creating a study plan
Replies
11
Views
3K
B Missing out on intermediate algebraic steps
Replies
23
Views
2K
Courses Would Calc 3 + Engineering Physics 1 be too much for Summer?
Replies
5
Views
3K
Tutoring Physics? (one bad experience, need to improve)
Replies
18
Views
5K
Schools Struggling with first year college (maths/physics)
Replies
5
Views
2K
Using a Problem Solving Technique for a simple word problem
Replies
24
Views
3K
Struggling in Precalculus: How to Get Back on Track for a Successful Math Career
Replies
6
Views
3K
Stupid Errors on Tests: How to Avoid Them
Replies
10
Views
3K

Hot Threads

Recent Insights

Back
Top