Sixth grade students have mastered the four operations of mathematics -- addition, subtraction, division and multiplication. By the end of the year, these middle school students have used these operations with decimals, fractions and negative numbers. At this point, math also involves reasoning, building on knowledge and observing; these skills are encouraged by higher level questions and participation from the students in a collaborative setting.
Asking open questions is a way to provide an opportunity for your students to think critically. For example, asking the sixth grade students how many polygons they can make with an area of 24 units is an open question. A closed question with the same objective is to have a polygon drawn and ask them the area of that polygon. Open questions can have more than one answer, and differentiation occurs automatically with this type of question. The more advanced students search for many ways to construct the polygon and answer the question. Other students also try to find a polygon to meet the criteria, realize that finding the many answers is valued, and continue working. Discussion of the different ways to answer the open question adds value to the question in the sixth grade classroom.
In Bloom's Taxonomy, a collection of verbs is divided into levels of thinking. Appraise, compare, contrast, criticize, differentiate, discriminate, distinguish, examine and question are verbs from Bloom's "analyzing" level, which encourages critical thinking. For example, having your sixth graders compare the distances around various circles' circumferences to their diameter measurements is a great introduction to pi and the formula for the circumference of a circle. It is also a critical thinking question which promotes exploration.
Great questions are wasted if wait time is not given for the answers. Too often teachers don't allow the students time to think and answer, blurting out the answer themselves or calling on another student. Some sixth grade students need more time to formulate their answers. Teachers should provide a few seconds of wait time for students to process the question and their answer.
Math builds on prior lessons. Critical thinking questions should help the sixth grade students see those relationships and connections. Teachers should ask students how the problem they are working on is connected to something they learned previously. For example, when your sixth graders are learning about ratios, you can remind them of their study of similar triangles. By asking them to think of how ratio and similar triangles are connected, the students are led to review what they have already learned about similar shapes and apply it to the study of ratios. The teacher helps the students to see the relationship between the two concepts and to deepen their understanding through the connections.