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9.1M Ability to support and reinforce the instruction of students in math following written and oral lesson plans developed by licensed teachers.
9.2M Ability to utilize effective developmental, age-appropriate, and culturally sensitive instructional strategies in math that supports the instruction of licensed teachers.

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Concept in Action

Strategy: Using an Inquiry-based Approach with Individual Practice

Strategy Components








Strategy To Go

Purpose of Strategy

Teaching students to think critically is a goal for most modern curricula. The goal of this type of pedagogy, inquiry-based instructionglossary icon, is to train a person to be able to analyze and synthesize past knowledge to comprehend a new concept. Curricula in the past did not address this process, using rote memorizationglossary icon and endless rehearsal to educate. This strategy will explore the teaching approach that fosters critical thinking applied to a single student. Many times the paraprofessional deals with students individually. The concept behind this type of teaching is based on the use of scaffolding questions that get a student to think critically. The class that uses this type of instruction is recognized by the teacher’s use of these scaffolding questions. If the teacher asks the students “why” or “how” questions, there is a good chance that the class is designed to foster critical thinking. This strategy is the application of this type of instruction with an individual student.


Upon completion of this strategy, the paraprofessional will be able to assist an instructor in teaching mathematics using an inquiry-based approach with individual practice.

Context for strategy

This strategy can be used in all grades, but it is more beneficial to students in upper level grades (at or above fifth grade) becauseA paraprofessional works with a student at his desk they are able to use abstract thought to solve problems. This does not mean that lower level grades cannot use critical thinking, nor does it mean that educators should stay away from scaffolding questions when teaching students in the fifth grade and lower. Students need to be trained to use the necessary cognitive processes to develop a sense of abstraction and to participate in mathematical discussions. Therefore this teaching strategy can be observed in all grades.

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Effectiveness of Strategy

There has been much research on student use of critical thinking. This method helps students retain the knowledge being taught as well as increasing cognitive processes, thus extending into all phases of the student’s life. Inquiry-based instruction has been found to foster the learning of content and process simultaneously (Woolfolk, 2001). It gets the students to formulate hypotheses, collect data, draw conclusions, and reflect on the process in problem solving (Pasch, Sparks-Langer, Gardner, Starko, & Moody, 1991). The challenge of this type of learning on the student is great, but the results are stellar. The instructor’s role is also a challenge. To be sure all students are engaged and challenged takes a great deal of preparation and organization, along with observational assessment techniques (Kiindsvatter, Wilen, & Ishler, 1988).

Strategy Summary

When a teacher teaches critical thinking in a math course, it is essential that the paraprofessional apply this same approach to keep the student at ease with a familiar pedagogical style. This also is true conversely. If a teacher does not use the critical thinking approach to teaching, the students will be uncomfortable with this process and it will hinder learning. If it is determined that the instructor is using scaffolding questions to elicit critical thinking and the classroom circumstances have led the paraprofessional to assist in the education of an individual student, the paraprofessional should begin by asking the student to describe the concept being taught. This will give the paraprofessional an overview of the knowledge this student has on the subject. This assessment will reveal any holes or misconceptions that the student has perceived.

When there is a missing building block in the concept, this piece of knowledge can be revealed through questions asked of the student by the paraprofessional. These scaffolding questions are based on past knowledge that the student acquire and are designed to make the student think critically about the missing pieces. If the problem lies in the misuse or misconception of a procedural step, the paraprofessional goes directly to that step and questions the student on why he or she believes that this is the right direction to take this problem. The most difficult aspect of this type of instruction is devising the scaffolding questions needed to get the student to choose the correct path to solve a problem. Identify the goal necessary to lead the student through the correct procedure, and ask questions centered on what can be done to achieve this goal.

Strategy Step-By-Step

Suppose Mrs. Langley teaches a 6th-grade course in mathematics, and Miss Boyd is working as a paraprofessional in this classroom. Mrs. Langley is a strong supporter of teaching using scaffolding questions to build the students’ abilities to think critically.

One student, Brad, is struggling with the concept of finding similarities between similar geometric polygons. Miss Boyd notices that this student is struggling and asks him what are the characteristics of one of the polygons. The student replies that each polygon is a triangle. Miss Boyd then asks what makes each figure a triangle. Three sides and three angles is the response. The paraprofessional asks if there are any other characteristics that make each figure a triangle. The student does not see any, so Miss Boyd draws the following figure (Figure 1) and asks the student if it’s a triangle. There are three sides (AD, BD, and CD) and three angles (<ADB, <BDC, and <ADC).

The student immediately claims that triangles must be polygons and this is not a polygon since it is not a closed figure. Miss Boyd then lists the three properties of the triangle: three sides, three angles, and polygonal characteristics. The student understands then that these are three of the properties that he can compare in the similar polygons. Through a quick inspection of the triangles he notices that angles are equivalent in similar objects and each shape must be the same polygon, but the sides are not equivalent. Miss Boyd congratulates the student on a job well done. She also asks him to see if he can find any relation between the sides of each polygon. She then goes on to the next student to see how she's progressing.

Figure 1 A diagram with three lines stemming out from the letter ‘D’ that is at the base. Each line leads to each of the letters ‘A’, ‘B’, and ‘C’

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Strategy To Go

Inquiry-based approach in an individual practice setting

  • Find the student’s error in the process of solving of a given problem.
  • Ask the student questions that he or she can answer using prior knowledge and will lead the student to the desired solution.

Questions to consider when implementing this strategy:

  • Would this strategy work with this/these student(s)? Why or why not?
  • If not, how would the setting or characteristics of the students need to be different in order to apply the strategy?
  • Why would this work?
  • If the strategy could be applied to the students(s), would it be a benefit at this time? Why or why not?

printer icon Get this Strategy To Go that you may print for future reference.


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