ACE-MCentral to the PENS Project is the model of successful problem-solving that we have developed. It is rooted in well-established paradigms of problem solving.
One is the problem-solving method of George Pólya:
- First, you have to understand the problem.
- After understanding, then make a plan.
- Carry out the plan.
- Finally, look back on your work to generalize.
A: Analyze the Task- interpret and understand what is provided in the task/problem. Suggestions often include annotating the task, creating alternate representations, and identifying the relevant information given in the task, including the task goal.
C: Create a Plan- connect the given information and desired result with models/ concepts/relationships. The solvers are making assumptions and establishing connections and intermediate steps between the given information and goal.
E: Execute a Plan- Follow the plan until the desired result is attained.
M: Monitoring- Ask questions to determine when there is an error, when to proceed to a new phase of the solution pathway, or when there is something missing or misunderstood in one’s own knowledge, skill or belief structure. The inclusion of monitoring transforms what might be a monologue into a dialogue as the solver constantly seeks to identify ways to improve the solution and his/ her understanding through the verbalization of questions and decisions.
In genuine problem-solving, the solver does not necessarily proceed through these components in a linear fashion. The most successful students do not solve a problem A-C-E, rather they may look more like A-C-A-E-C-A-E, etc. It is the monitoring that guides the solver when to move from one component to another. The most successful students employ monitoring through a solution.
ACE-M has been employed in chemistry, mathematics and physics classrooms with great success. Students in a recent introductory physics course were particularly appreciative, with thirty-three of the thirty-seven students describing ACE-M as “helpful”. Below are a few student quotes about ACE-M:
- “It was pretty helpful. At first I really did not follow it but when I did start to, I notice that it really helped in solving the difficult problems.”
- “The ACE-M method got me on track and helped me on difficult problems that I would've been lost on.”
- “I thought that this method was very helpful because it provided me with a step by step process to solve each problem. It was a good reminder to have so that I would not try to go straight to plugging in numbers into whatever equation I had in front of me.”
- “I think my problem solving abilities have definitely improved after this course. I am now able to look at a problem more critically and better understand what the question is really asking for.”
- “At the beginning of the semester, I was ok at solving problems, but most of the time I would just plunge ahead without really thinking about if what I was doing made sense. Now I try to stop myself every once in a while to check and make sure that the equations I'm using and numbers I am getting make sense.”
- “I feel like I am much better than I was at the beginning. I don't freak out when I see a word-problem. I just take everything sentence by sentence and try using the knowledge I have to find a way to solve it.”