Mr. Ho's Math Fusion

(Traditional Direct Instruction + Thinking and Flipped Classroom Philosophy)

What is Mr. Ho's Math Fusion?

Mr. Ho's Math Fusion is a teaching method, proposed in February 2024, which combines traditional direct instruction with part of Dr. Peter Liljedahl's Building Thinking Classrooms (BTC) teaching philosophy and part of the Flipped Classroom teaching philosophy within a daily Math lesson. Its goal is to establish a balance between these teaching methods within the daily Math lesson so that the teacher can reach all students in an equitable and inclusive classroom through an anti-oppression lens. This balance should differ from class to class, as it depends on many factors such as:

the lesson topic(s) and learning goals of the day,
the learning strengths, needs, preferences, and styles of the students,
the readiness of the students to learn the lesson topic(s), and
the teacher's teaching preferences, styles, and experiences.

When this balance of teaching methods is established in the classroom, students will feel welcomed and respected and have a sense of belonging, thus enabling them to achieve the best of their ability and experience many "aha!" moments in their learning.

How does Mr. Ho's Math Fusion classroom look?

Mr. Ho's classroom setup in his Math Fusion model is very similar to Dr. Peter Liljedahl's thinking classroom model, as it is for collaborative work and peer learning. The student desks are arranged in groups of 4, and vertical non-permanent surfaces (VNPS) are available around the classroom so that students can work collaboratively on math problems. However, unlike Dr. Peter Liljedahl's defronted classroom model, Mr. Ho's Math Fusion classroom has a front that allows the teacher to do a short and meaningful introductory lesson before sending students to VNPS to work on the in-class questions of different levels of difficulty (i.e., mild, medium, and spicy).

Here is a short video clip showing Mr. Ho's classroom setup:

2024-25 Mr. Ho's Math Fusion Class.mp4

How does Mr. Ho's Math Fusion work?

In Mr. Ho's Math Fusion classroom, a teacher will:

1. use Flippity to assign students to visibly randomized groups of 3 or 4 (Dr. Peter Liljedahl's BTC philosophy)
2. give a short and meaningful introductory lesson so that students acquire some basic knowledge of the lesson topic(s) for the class (traditional direct instruction)
3. send students to the vertical non-permanent surfaces (VNPS) (Dr. Peter Liljedahl's BTC philosophy) to engage in active learning by working on in-class questions.

These in-class questions are like the homework questions assigned to students to work on at home in the traditional way of learning, except that in Mr. Ho's Math Fusion, students will do these questions during class so that they can get the maximum support from their teacher and classmates (or learning partners) (the rationale for the flipped classroom model).

In addition, these in-class questions have three different levels of difficulty: mild (basic), medium (intermediate), and spicy (advanced) (Dr. Peter Liljedahl's BTC philosophy), which are designed to gradually guide students from mimicking their teacher's procedure of solving a Math problem in the introductory lesson (mild/medium) to exploring new skills (spicy) or synthesizing different ideas into new ones. Thus, this would help them develop higher-order mathematical problem-solving skills.

1. give descriptive and meaningful feedback on students' work on the VNPS, whenever applicable.

According to Dr. Peter Liljedahl's BTC philosophy (Chapter 5, "How we answer questions in a thinking classroom," in his BTC book), the teacher should not answer their students' questions that would stop any thinking. However, this does not mean that the teacher should not answer any questions from their students during the class. This is a major misconception made by some teachers.

The teacher should make their professional judgment to answer questions that would support their students' thinking or learning directly or indirectly and foster a positive and welcoming learning environment in the classroom for students with different learning needs and/or preferences. This is like what Dr. Peter Liljedahl said about the importance of having a balance between challenge and ability in the classroom (Chapter 9, "How we use hints and extensions in a thinking classroom," in his BTC book). This judgment should be considered on a case-by-case basis. In practice, it is found that exceptions often need to be made in a diverse classroom; otherwise, students would get discouraged from learning.

1. consolidate the learning goals near the end of class and, if necessary, provide optional check-your-understanding questions for students to practice (Dr. Peter Liljedahl's BTC philosophy).

Mr. Ho's Math Fusion Model:

How does Mr. Ho's Math Fusion provide students with a successful learning journey?

Mr. Ho believes that a successful learning journey for students consists of four phases: (1) observation, (2) active learning, (3) consolidation, and (4) further reinforcement. In the observation phase, the students observe how a teacher solves a math problem so that they can acquire the basic or foundational skills. Through observation, they also learn the proper mathematical form and notation, as demonstrated by their teacher. In Mr. Ho's Math Fusion model, this observation phase takes place when the students observe the teacher presenting a short and meaningful introductory lesson at the beginning of the class.

After the observation phase, the student learning journey goes into the active learning phase. In this phase, students are actively involved in their learning. They first need to practice the skills that they observed in the introductory lesson by mimicking their teacher's procedure of solving a Math problem. Once they successfully acquire the basic or foundational skills through mimicking, they can then move on to solve higher-order thinking questions by exploring new ideas or synthesizing different ideas or concepts into new ones. In Mr. Ho's Math Fusion, this active learning phase takes place when the students are working collaboratively in visibly randomized groups on the in-class questions at VNPS, starting from the mild and medium levels of difficulty (i.e., mimicking) to the spicy level of difficulty (i.e., exploration). While the students are working on VNPS, the teacher listens to the students' discussions, reads the students' work on VNPS, and indirectly supports the students. The teacher also takes notes on what the students struggle with and uses the notes to plan for the next day's lesson to support the students (assessment for learning).

Next, the student learning journey goes into the consolidation phase. In this phase, students share their ideas and methods for solving problems with each other, or the teacher gives students a consolidation task that allows them to check their understanding of the learning goals of the day and assess by themselves (assessment as learning) how much they learned on that day.

After that, the student learning journey reaches the further reinforcement phase in which they do the optional check-your-understanding questions at home for practice, thus reinforcing the concepts and skills they learned in class.

Mr. Ho believes that if the students successfully go through these four phases of the learning journey, they will have the best learning experience and will be able to achieve their highest potential. Thus, Mr. Ho's Math Fusion creates the conditions of success for students.

What about Mr. Ho's students in action in his Math Fusion classroom?

To see Mr. Ho's students in action in his Math Fusion classroom, check out the following subpages:

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