#190 Atomisation and Unstoppable Learning with Kris Boulton
May 1, 2024
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Expert Kris Boulton discusses atomization in education, breaking down complex processes, teaching methods using taxonomy concepts, identifying mathematical 'atoms' for better instruction, simplifying math expressions, teaching concepts using examples and definitions, importance of examples in teaching, teaching quadratics with examples, using correlated features in teaching, teaching strategies with minimally different examples, and the power of atomization in enhancing student learning.
Atomizing math concepts helps combat expertise-induced blindness and aids student understanding.
Breaking down complex math processes into simpler steps facilitates learning and comprehension.
Using a taxonomy of seven concepts in teaching math enhances student engagement and learning outcomes.
Identifying and teaching mathematical 'atoms' improves instruction effectiveness and student comprehension.
Teaching math by breaking concepts into smaller 'atoms' supports student understanding and confidence building.
Utilizing examples, non-examples, and clear communication enhances teaching effectiveness and student learning.
Deep dives
Categorical Concepts: Identifying Types of Objects
Categorical concepts refer to classifying objects into specific types based on their characteristics. For example, differentiating between shapes like triangles, cylinders, or prisms is a categorical concept. Teaching students to identify whether an object fits a specific category, like asking if something is a triangle or a prism, helps in developing their understanding of distinct types in mathematics.
The Importance of Non-Examples in Learning Categories
Non-examples play a crucial role in learning categories as they help distinguish what does not belong in a specific category. By providing examples of what does not fit a category, students develop a clearer understanding of the defining characteristics of that category. For instance, showing examples of objects that are not prisms alongside prism examples reinforces the unique features of prisms, aiding in better categorization.
Prism Example Sequence: the Power of Non-Examples
Experimenting with a prism example sequence highlighted the power of non-examples in clarifying categories. By showcasing various prism types as well as objects that do not fit the prism category, students were able to grasp the defining features of prisms more effectively. This hands-on approach demonstrated the impact of incorporating non-examples in teaching categorical concepts for clearer understanding.
Initial Teaching Sequence
In the initial teaching sequence, the speaker presents examples to the students, explaining how to respond correctly. The examples are structured in a way that allows for the students to generalize the concept further from what is shown.
Testing Sequence
The testing sequence is used to assess whether the communication in the initial teaching sequence was successful. Examples presented in the testing sequence vary, with a mix of correct and incorrect responses, ensuring that the students demonstrate their understanding of the concept.
Expansion Sequence
The expansion sequence involves presenting new and progressively more complex examples to the students, challenging them to apply the generalized concept to varied scenarios. Each question in the expansion sequence introduces a twist or a new element, allowing students to demonstrate their deep understanding of the concept.
Reflection
The speaker uses a hands-on approach to teaching, encouraging active participation and critical thinking. By structuring the teaching into initial, testing, and expansion sequences, the students are guided through a learning process that builds on their understanding incrementally. The emphasis on lowering the stakes and creating a supportive learning environment fosters confidence and engagement among the students.
Implementing Cognitive Routines in Teaching Mathematics
Implementing cognitive routines in teaching mathematics involves key principles like starting with non-examples, identifying concepts distinct from facts, and utilizing silence in the classroom to enhance learning. Teachers can try starting with non-examples as a simple yet effective strategy to engage students. Additionally, breaking down concepts into distinct atoms and focusing on clear communication can help streamline the learning process. Emphasizing the use of silence and narrating key steps during instruction can also enhance student engagement and understanding.
Overcoming Teaching Challenges and Scaling Atomized Instruction
Scaling atomized instruction in schools facing challenges like understaffed math departments can be daunting. However, with proper training and support, teachers at all levels can adopt atomized teaching strategies effectively. Providing training focused on key principles like starting with non-examples, identifying concepts, and utilizing silence can empower teachers to implement atomized instruction in their classrooms. Collaborative efforts, resource development, and ongoing professional development can further support the scalability of atomized teaching approaches across schools.
Break Down Concepts into Atoms for Effective Learning
Breaking down complex concepts into smaller, manageable parts, known as atoms, can greatly enhance student understanding and learning. By focusing on individual atoms and carefully sequencing examples, teachers can create a more targeted and effective learning experience. Emphasizing the importance of thoughtful planning and concise language during instruction to ensure clarity and efficiency in teaching.
Balancing Technical Language and Conceptual Understanding
Prioritizing student comprehension over mastery of technical terminology can lead to deeper learning outcomes. Chris Bolton's approach highlights the significance of students being able to articulate concepts rather than just knowing the formal definitions. This emphasis on understanding concepts before delving into technical language allows for a more intuitive grasp of complex ideas and promotes a solid foundation for future learning.
Kris Boulton returns to the podcast to discuss atomisation and how it can lead to unstoppable learning for our students. You can access the show-notes here: mrbartonmaths.com/blog/atomisation-kris-boulton
Timestamps:
Atomization in mathematics education, with a focus on expertise-induced blindness and its impact on students' understanding. (10:57)
Breaking down complex processes into simpler steps. (15:12)
Teaching methods using a taxonomy of seven concepts (categories, comparative, transformation, fact, and process). (19:40)
Categorical concepts, comparatives, and transformations in mathematics. (23:43)
Identifying and teaching mathematical "atoms" for better instruction. (29:38)
Teaching math concepts by breaking them down into smaller, familiar "atoms" to help students understand and build upon them. (38:18)
Simplifying math expressions using factoring and atomization. (44:09)
Teaching math concepts by breaking them down into smaller, more manageable "atoms" to help students understand and build confidence. (49:48)
Categorical concepts in math education, with a focus on non-examples. (53:43)
Importance of examples in teaching, with a focus on the limitations of language in conveying concepts. (57:31)
Teaching concepts using examples and definitions. (1:03:31)
Using correlated features in math teaching. (1:08:50)
Teaching quadratics with examples and caveats. (1:13:28)
Using examples to teach concepts, including minimally different and maximally different examples. (1:19:20)
Teaching language learners using negative examples first. (1:27:01)
Teaching math concepts using examples and testing sequences. (1:31:20)
Decisions and categorization in math education. (1:35:10)
Using language to make math problems easier. (1:39:51)
Differentiating between cognitive routines and transformations in math. (1:45:04)
Teaching math concepts using different methods. (1:48:25)
Teaching math concepts to children using a step-by-step approach. (1:54:18)
Using mini whiteboards for testing sequences in math class. (1:59:19)
Teaching strategies, emphasizing the importance of interactive learning and using whiteboards. (2:02:36)
Using simplified symbols vs. expert-level symbols in math education. (2:07:59)
Using continuous conversion in math lessons. (2:12:00)
Teaching math concepts using cognitive routines. (2:20:02)
Teaching math concepts to students using explicit and implicit methods. (2:25:28)
Teaching strategies, including non-examples, identifying concepts, and managing classroom noise. (2:32:03)
Math education, examples, and training. (2:35:28)
Improving math education with technology and hybrid learning models. (2:39:19)
Teaching methods and classroom management. (2:43:42)
Teaching math to mixed-ability students, emphasizing the importance of exploration and unveiling mathematical concepts. (2:50:08)
Teaching math to high school students, focusing on approach for different learners. (2:53:42)
Teaching probability with creative problem-solving strategies. (2:57:47)
Breaking down complex math concepts into smaller parts for better understanding. (3:01:57)
Sequencing examples in teaching, emphasizing clarity and brevity. (3:06:53)
Using "atomization" to teach math concepts more efficiently. (3:11:09)
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