Provide hands-on activities that allow students to share ideas and feedback with one another.
Diagnostic teaching is an ongoing assessment of students as they are learning in order to teach -- and reteach as necessary -- concepts for comprehension. Teachers using diagnostic teaching look at a student's performance in the subject to plan appropriate learning activities. Using diagnostic teaching methods in math leads to better mastery and a longer retention of mathematical concepts by students.
Diagnostic Testing
A teacher should test the students to determine their abilities before teaching new concepts. For example, a teacher who wishes to teach elementary students to multiply double-digit numbers must first test the students for understanding of place values and their mastery of basic multiplication facts. Most math books contain pre-tests and post-tests that can be used for diagnostic testing. Such tests should evaluate the specific skill the teacher wishes to target. A teacher can analyze the results of the test to plan lessons appropriate for mastering mathematical skills.
Checking for Understanding
Diagnostic teaching calls for the continual assessment of students' abilities. Checking in with the students for understanding during teaching is a good way to tailor a lesson to their needs. Checking understanding can be done in a variety of informal ways that can allow a teacher to quickly assess the progress of the students. Ask students to "signal" their understanding; students can use thumbs up or thumbs down, hold up their fingers or point to the correct answer. Students can also use slips of paper or whiteboards to hold up answers while the teacher circulates the room and checks the responses. Teachers can also call on individual students and have them answer questions to gauge their understanding.
Revisiting Concepts
Once teachers have assessed student learning and pinpointed areas of misconception, confusion and error, they can begin to plan appropriate lessons for reteaching the concepts. These lessons should revisit areas in which students have shown difficulties. Focus each lesson on one concept and provide activities in which children can apply what they are learning in real life situations whenever possible. For example, when teaching elementary students add and subtract decimals, set up an area of the classroom as a store and have students take turns being the shoppers and the cashier.
Provide Feedback
In order to use diagnostic methods effectively in the classroom, teachers must provide their students with valid feedback. Feedback should be given as soon as possible so that students can recognize the areas they need to work on. Students can also provide feedback to on another. Good feedback is more than telling a students if the answer is right or wrong; it allows students to discuss why it's right or wrong and explore other methods of obtaining the correct answer. Students can help one another work out problems and tell one another whether they think they are doing it correctly. Students can work on math problems in small groups or the teacher can lead a group discussion based on methods for solving the problem.
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