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Lear Cook

Hampton City Schools

Geometry encompasses a range of concepts that we all encounter in everyday life. However, students struggle with understanding the basics of geometry and its application. State and local data, along with classroom observations, was used to diagnose some of the causes of the low scores on assessments. It is found that the lack of engagement and real-world application are factors hindering understanding and transference of geometric knowledge. It is recommended that teachers engage students in classroom  activities that will increase understanding, connect classroom  learning to the real world, and provide the opportunity to  infuse learning from other subjects.


Interested in exploring ways to increase student engagement and discourse? State data for geometry decreased by two percentage points between the 2015-2016 and 2016-2017 school years. The skills for the different activities in this session are based on the lowest pass rates reported by Virginia Department of Education (VDOE) on the 2016-2017 state geometry assessment. This session showed teachers how to effectively incorporate cooperative learning activities and ideas into a lesson by using group activities, problem-based activities, and games to explore and/or review concepts. The activities were based on Hattie’s Effect Sizes Teaching/Instructional Strategies, Learning Strategies, and Strategies Emphasizing Feedback.

Problem-solving teaching uses problem-based and/or project-based activities. The Discover It activity uses the Concrete-Representation-Abstract (CRA) sequence of instruction that allowed participants an opportunity to use Exploragons to complete a series of activities. Each participant used the Exploragons to construct congruent triangles, similar triangles, and to explore the Triangle Inequality Theorem. Guided questions accompanied the activity to keep the participants on track. Participants, in addition to creating the triangles using the manipulative, were encouraged to write down their thoughts and questions. Participants were paired so they could compare and contrast the triangles they created and compare and contrast their  pictures or drawings. The discourse during this portion of the activity gave each person a chance to verbalize his or her understandings, discoveries, and questions in a safe environment. To close the activity, each participant had to independently complete a problem abstractly.

Deliberate teaching practices that use well thought-out activities can connect the learning objective  with success criteria. The learning objective needs to be specific. The Organize It activity for this session focused on note taking. The note taking uses a foldable booklet with interactive notes that guides the participant and provides  differentiation so all students have access to important   information. There is one book per skill and each booklet is glued onto a 3-whole punch cardstock sheet to support  notebook organization. Each booklet included guided practice and independent practice for  the skills taught in the lesson.

The Practice It activity uses the gallery walk strategy to get participants up and working. The gallery walk guides participants to their next problem to solve. Each person is responsible for working each problem. The skills covered in this activity were based on all of the Standards of Learning (SOL) for geometry. The format followed the SOL and students can use the CRA model to easily solve 5 out of 9 problems. The participants were allowed to discuss the problems but not share their answer. The discussion between the participants were beneficial.. Once the procedures were learned , participants had the opportunity to apply their new skills  to a real-world scenario.

Classroom discussion has the highest impact on student achievement of the three factors and it is the easiest to implement. The transition between each activity was “Which One Does Not Belong?” Four images with overlapping characteristics were displayed with no verbal instruction. When the supplies were collected, participants discussed the four figures. The conversation was rich and informative. They asked each other questions, they provided feedback, and gave  different perspectives. The first four figures were based on Disney movies. Starting at this level builds confidence and allows all to be successful. The second set of images was based on congruent triangles. The discussion included more feedback to their peers than questions. The confidence level of some participants who were unsure of the solutions started to increase due to  the positive feedback they received from their peers. For the last four items, all participants were discussing which one did not belong.

Give a student the answer, and he or she remembers for a block. Teach a student to calculate the answer and they remember for a year. Have a student discover

the answer through problem solving, and they remember the experience for a lifetime. -Lear Cook



Effect Size

Teaching/Instructional Strategies

  Problem-solving teaching


Learning Strategies

Deliberate practice


Strategies Emphasising Feedback

Classroom Discussion


Table 1: Hattie’s 2017 Updated List of Factors.

Geometry is a course connected to the world around us. Students need the opportunity to manipulate, engage, discuss, and make sense of the skills taught in the classroom. Making small changes to how new mathematical content is taught and discussed can increase student engagement and understanding. Using a problem-solving approach, which includes deliberate practice and discourse, improves how students see and connect with the mathematics.


Conctere-Representational-Abstract Sequence of Instruction. (n.d.). Retrieved from

Killian, S. (2017, September 24). Hattie's 2017 Updated List of Factors Influencing Student Achievement. Retrieved from

Virginia Department of Education. (n.d.). School Report Card. Retrieved from

Virginia Council of Teachers of Mathematics
PO Box 73593
Richmond, VA 23235 

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