Problem Solving Categories

December 20, 2019

Like fluency, application word problems fall into three different categories:

1. Immediate Review

2. Cumulative Review

3. Preparatory

Immediate review word problems address a topic that students are currently studying.  When children are required to recall recent learning using a new modality, they develop a more holistic understanding of the concept.

Practicing current topics through word problems builds understanding more powerfully than traditional homework or lesson reviews for two reasons.  First, engaging with word problems is a proactive experience.  Secondly, the stimulus opens more neural pathways to arrive at answers, i.e. drawing, reasoning, and calculating.  Both factors lead to happier math experiences and stronger learning.

Immediate review application problems are especially meaningful when addressing computational topics, because it provides relevance to a newly learned skill (see examples below).

Later in the school year, the same (or analogous) word problems can serve as a cumulative review.

Practicing the previous day’s content is not as useful on days following chapter reviews, tests, or holiday breaks.  It’s also not logical when a lesson did not go well and needs to be retaught.  On these occasions, teachers can use their problem-solving block to address concepts taught earlier in the school year without disrupting curricular flow.

In addition to addressing previously learned content, cumulative review word problems can also provide practice for modeling different types of diagrams.  First grade students might be introduced to ten-stick drawings early in the school year, but then go several months without seeing or drawing them.  Sometime during the winter or spring, their teacher might revisit the model to gauge how well their class remembers it (see example below).

During a long geometry unit, a fourth grade teacher might realize that their students haven’t practiced a sum/difference diagram for several months.  Therefore, they might find it more valuable to deliver a word problem that requires this type of model than incorporating the current topic into problem solving time (see example above).

Word problems can also serve as a catalyst to prepare students for the lesson(s) that follow.  Reacquainting children with prior knowledge in the minutes before a new concept is taught provides them with confidence and a foundation for deeper learning. It also allows the teacher more time to deliver the lesson.  These preparatory word problems work well as a lead-in to a new unit (see examples below).