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I surveyed mathematics teachers in Singapore to get perspective on the importance of using the C-P-A approach and technology in the classroom. 164 teachers responded.
Overall, the survey information indicated that:
Teachers wove in the C-P-A approach in mathematics lessons and revisited it often because students needed to see the relationship between concrete, pictorial, and abstract modes of representation in order to problem-solve and transfer mathematical understanding
The C-P-A approach engaged students in learning by drawing on their practical knowledge and assisted students in making connections between abstract mathematic concepts and real-world mathematics
When planning a lesson using the C-P-A approach, a teacher must take in several moderators:
the mathematics topic being taught
the instructional time needed to facilitate the construction of meaning
the developmental status of students
the type(s) of manipulative(s) being used
the level of instructional guidance
Low-progress students benefited the most from concrete experiences because manipulatives represented abstract concepts in a visual way and provided students with a strategy from which to work
Teachers of low-progress students preferred students to discover mathematical concepts and interact with manipulatives under direct instruction compared to unstructured exploration
Virtual manipulatives are useful for certain topics and engaged students in deeper learning, exploration, and peer discussions
Technology should be used purposefully and only if it provides an augmentation, modification, or redefinition of the math task (SAMR model)
Technology should encompass the 3 E's
Engaging (dynamic platforms provide more exposure to a variety of people and ideas)
Efficient (require less time to prepare and distribute materials, intuitive interface user audience)
Effective (teachers can curate tasks to meet the needs of each individual student)
I surveyed mathematics teachers at the biennial Teachers' Conference and ExCEL Fest 2023 (TCEF2023) on the importance of using the C-P-A approach and technology in the classroom after guiding teachers through a learning example using the C-V and V-P-A approach.
Results of the Survey
Results of the Survey
Section 1: Background Information
Kindergarten - 1 teacher (0.6%)
Primary 1 - 30 teachers (18.3%)
Primary 2 - 27 teachers (16.5%)
Primary 3 - 25 teachers (15.2%)
Primary 4 - 20 teachers (12.2%)
Primary 5 - 27 teachers (16.5%)
Primary 6 - 19 teachers (11.6%)
Secondary 1-4 - 15 teachers (9.1%)
The C-P-A Approach
The C-P-A Approach
Section 2: Common ways teachers implemented the C-P-A Approach to sequence learning and the understanding of mathematical concepts in their classroom
Start with hands-on learning experiences, link to pictorial diagrams, then move on to word problems
Start with tangible objects to showcase base concepts and encourage students to be part of the learning process, then motivate students to make connections to pictorial representations on worksheets
Start with a tangible way for students to test a theory or idea through trial and error
A list of common manipulatives used to teach particular concepts:
Use base-ten sets and number discs to develop place value understanding
Use play money to develop arithmetic involving money
Use weighing scales and rulers to teach mass and length
Use unifix cubes to demonstrate addition and subtraction concepts
Use cups and beans to demonstrate multiplication or division concepts
Use multi-link cubes to demonstrate multiplication or division concepts
Use fraction discs/bars/strips to teach equivalent fractions
Use interconnected straws to form angles and identify right angles, acute angles, and obtuse angles
Use Anglegs to form angles of different sizes/different degrees
Use multi-link cubes to teach isometric drawing of cubes, cuboids, and solids
Technology
Technology
Section 3: Most common technological resources used in Singapore classrooms ranked. Teachers had the opportunity to vote for more than one technological resource.
Student Learning Space (MOE's core platform) - 106 (64.6% of teachers listed this as one of their top resources)
Videos (i.e. Youtube, Khan Academy, Brainpop) - 91 (55.5%)
Quiz Platforms (i.e. Kahoot!, Quizizz) - 80 (48.8%)
Virtual Manipulatives (i.e. Geogebra, Desmos, Base-10 Blocks) - 71 (43.3%)
Games (i.e. Math Playground, Arcademics) - 39 (23.8%)
Presentation Tool (i.e. ClassPoint, Nearpod, Padlet) - 28 (17.1%)
Virtual Whiteboard (i.e. SMART Board, Zoom Whiteboard) - 21 (12.8%)
Microsoft Office 365 - 13 (7.9%)
Google Workspace/G Suite - 13 (7.9%)
Miscellaneous: Koobits/Blooket/Plickers - 13 (7.9%)
Communication Tool - 6 (3.7%)
Section 4: What is the value of teaching with technology?
Differentiate learning through multimodal features (content, process, and product)
Personalize learning by fostering student agency and creativity
Scaffold learning to support student thinking and guide interactions
Promote metacognition by integrating learning supports to regulate student thinking and reflection
Capture and analyze assessment data to provide actionable feedback (assessment for learning)
Enhance learning
Provide opportunities for students to communicate reasoning
Provide opportunities for self-directed/self-explored learning
Front-load new information prior to teaching synchronous lessons
Provide opportunities for blended learning
Provide opportunities for students to collaborate
Address different learning styles/multimodal types of learning
Aid students with specific needs through assistive technology
Teach students to be discerning users of technology
Make math more meaningful and relevant with real-world examples and visual aids
Provide all students the opportunity to equitably learn content
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