What do students think?

• 4 Intermediate Algebra sections (76 students)
• Start of Week 1, Fall 2023 - "What do you think it means for a number to" be a solution to an equation?"
• 8 out of 72 (~11%): "If you substitute a solution into an equation, it satisfies the equation, making the equation true."
• 12 out of 72 students (~17%) alluded to substituting a solution into an equation but did not expand further.
• The remaining responses were irrelevant/incorrect.

Intro/Test 1

• End of Week 1, Fall 2023 - Students engage with activity and scored an average of 87.13%.
• Week 4 - 74 students take Test 1.
• Solve \(\color{blue}\frac{41}{9}=\frac{5}{2}\left(x+\frac{2}{3}\right)-\frac{1}{3} x\) for \(x\). Explain whether the number you found for \(x\) was a solution to the equation. 
• 17 out of 74 students (~23%) were awarded at least half credit.

Test 2

• Week 7 - 74 students take Test 2.
• Which of the following values are solutions to the inequality \(\color{blue}9 \leq 3 x+4\) ?
  I. \(\color{blue}-7\)                    II. \(\color{blue}8\)                    III. \(\color{blue}2\)
• Students encouraged but not required to revisit the activity from the start of the course. 
• 59 out of 74 students (~80%) were awarded at least half credit.

Test 3

• Week 11 - 51 students attended class on Solving Rational Equations.
• Solve \(\color{blue}\frac{n}{n+3}+\frac{1}{n-4}=\frac{6-5 n}{n^2-n-12}\) for \(n\).  
• Initially asked to work on this problem independently.
• Without being prompted to do so, 36 out of 51 students (~71%) verified \(n=1\) was the only solution to the equation and also wrote an explanation.

Final Exam

• Week 15 - 50 students sat for the Final.
• Solve \(\color{blue}\sqrt{2 x+2}=3+\sqrt{2 x-1}\) for \(x\).  
• 33 out of 50 students (66%) correctly identified the equation has no solutions. 4 more students solved the question correctly and verified the candidates but did not explain their findings.
• Historically, maximum of ~25% with semesters with at least 65 students and average of ~19%. 
• Similar results in Spring 2024.