During this class, we learned about the five types of purposeful questions. The first type is gathering information, which teachers use when want students to recall basic facts or definitions (mostly things that are memorization). This is a question used to assess students because it usually has a right and wrong answer and can help the teacher gauge whether or not the student understands. The second type of purposeful question is probing thinking, which is used when teachers want students to explain, elaborate, or clarify their thinking and reasoning and why they came up with that answer. The third type of purposeful question is making mathematics visible which teachers use when they want students to make connections between mathematical concepts or ideas. This question allows students to connect the topic to other topics they have already learned which expands their knowledge and helps them make connections. The fourth type of purposeful questioning is encouraging reflection and justification which is used when teachers want to get a deeper insight into the students thinking and reasoning. Teachers often use this question for students to argue the validity of their work and make them think about why the answer they got is correct. The fifth and last type of purposeful question is engaging with the reasoning of others, which teachers use when they want students to learn from the reasoning of their peers. This requires students to think about things in the way their peers did which may be different than their own reasoning. It is important for teachers to anticipate questions their students may ask so they can be prepared to explain things in a different way if students aren’t understand. This may include using manipulatives or other teaching strategies which is hard for teachers to come up with on the spot. It is also important for teachers to answer questions using other questions instead of just giving students the answer because it requires students to think about why that is the answer and helps them gain a deeper understanding of the mathematics. Students are also more likely to remember something they discovered themselves than a simple answer from the teacher.
Using manipulatives in elementary mathematics is extremely important for students to gain a conceptual understanding of a variety of mathematical topics. It can be difficult for teachers to determine if students can transfer their understanding from manipulatives to other situations but this is why teachers need to plan time to have students learn the concepts with the manipulatives and then give the students time to solve the problems and only use manipulatives to check their work before finally removing the manipulatives and assessing the student’s knowledge because they won’t usually have these manipulatives in higher grades and outside of the classroom. In order to assess this growth and understanding, teacher observation and questioning are crucial. Teachers need to walk around the classroom or pull individual students or small groups and have students demonstrate their thinking with and without manipulatives. Manipulatives are also great because they help students improve their
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