Central 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:
  1. First, you have to understand the problem.
  2. After understanding, then make a plan.
  3. Carry out the plan.
  4. Finally, look back on your work to generalize.
These are critical phases for any successful problem-solver to employ, regardless of subject. While they are necessary, they are not sufficient. Since Pólya’s pioneering work, researchers have identified additional phases found in successful solutions. One of the most important in problem-solving is monitoring one’s understanding and actions, which is part of the broader concept metacognition, which is an awareness of, and ability to regulate, one’s own cognitive processes. Our model, which we use as the basis of instruction and assessment, combines these two aspects into one- ACE-M.

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.”
Students reported an increase in their problem-solving self-efficacy:
  • “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.”