Trends

​Unit 3: Math Ed 525

By Bed Prasad Dhakal

Applied Mathematics

​Definition

1. Definition 1

2. Definition 2

3. Definition 3

4. Definition 4

Multiple Choice

A Nepali curriculum developer argues for including topics like statistics and linear algebra in the secondary curriculum because of their wide use in economics and social sciences. This argument aligns most closely with which definition of applied mathematics from the text?

• Definition 1: classical applied mathematics

• Definition 2: significant practical applications

• Definition 3: applied in some other field or in real life

• Definition 4: mathematics in livelihood

Multiple Choice

If a hydropower project in Nepal uses complex differential equations to model water flow and turbine efficiency, this would be an example of

• The 'New Math' movement, as it unifies different mathematical fields

• Ethnomathematics, as it relates to a specific cultural context

• Pure mathematics, as it involves abstract concepts

• Classical applied mathematics, as it uses calculus and differential equations

Multiple Choice

A Nepali teacher, frustrated with students forgetting geometric formulas, decides to have them design and calculate the materials for a model of a local stupa. This pedagogical shift reflects the argument that mathematics is better understood and retained when it is

• Separated into compartments of arithmetic, algebra, and geometry

• Focused on preparing for calculus

• Presented in an applicable form

• Taught in a purely abstract and rigorous manner

Rationale: Why to Teach Applied Mathematics?

According to

1. For motivation

2. For cultural reason

3. As a service subject

4. Recognition of structure in the presence of noise

Multiple Choice

A teacher in a rural Nepali school uses the local context of calculating the required amount of seeds for a terraced farm to teach concepts of area and ratio. According to the text, what is the primary rationale for this approach?

• For motivation

• For cultural reason

• For recognition of structure

• As a service subject

Multiple Choice

A community forestry group in Nepal wants to estimate the volume of timber in a forest patch. They model the tree trunks as frustums of cones. This act of simplifying a complex, irregular shape into a standard geometric form is an example of

• A cultural application of mathematics

• A service subject application

• Recognition of structure in the presence of noise

• Pure mathematics

Trends in Teaching Applied Mathematics

1. Modeling-First Approach

2. Interdisciplinary Projects

3. Technology Integration

4. Inquiry- Based Learning

5. Trends at primary level (512)

6. Trends at secondary level (1316)

Multiple Choice

The text describes a trend in primary education, influenced by figures like Montessori, that moved away from the 'talks and chalks' method. What is a key feature of the new classroom layout and method?

• A strict focus on abstract concepts and rigorous proofs from a young age

• Children are not allowed to make mistakes to ensure accuracy

• The teacher acts as an advisor and consultant, moving around the classroom

• Children sit in separate desks facing the teacher to ensure focus

Challenges in Teaching Applied Math

The philosophy behind using applied mathematics in teaching is that students learn through mistakes. As the task in applied mathematics is practical, students get hands-on

experience added by intellectual exercise. 

But in pure mathematics most of subject taught are rigorous and abstract.

1. Visible Struggles

2. Classroom Challenges

3. Instructional Barriers

4. Curriculum & Resource Gaps

5. Systemic Causes

Challenges in Teaching Applied Math

Multiple Choice

According to the text, one of the significant problems in teaching applied mathematics is that

• Some mathematics teachers are ignorant of other disciplines

• Students are inherently not motivated by real-world problems

• Pure mathematics is always more useful in the long run

• There are not enough real-world problems to use as examples

The Impact of Applied Mathematics in Education

1. Improved conceptual understanding

2. Higher student engagement and retention

3. Development of transferable skills (e.g., data literacy)

4. Better preparation for higher education and careers

The Impact of Applied Mathematics in Education

• Problems and problem-solving in the schools

• Mathematical subject matter in the schools

• The possible effect of applications on pedagogy

• Applications and teacher training

• Application of math and vocational education

Multiple Choice

The text mentions an internship in industry as a part of teacher training in some countries. What is the primary purpose of this initiative?

• To allow teachers to learn how mathematical sciences are really applied

• To ensure teachers are familiar with the latest pure mathematics research

• To reduce the amount of time teachers spend in university

• To help teachers earn a higher salary

Mathematical Modeling

Example 1 (River crossing)

A farmer has a goat, a cabbage and a pet wolf to ferry across a river, but the boat will take only her and one of the three things. The goat cannot be left alone with either the cabbage or the wolf. How does he do it?

Mathematical Modeling

Example 2 (Largest volume)

A rectangular sheet of light metal is to be cut and bent to form an open-topped box.

How should it be cut to create a box with the largest volume?

Mathematical Modeling

Example 2 (Largest volume)

Mathematical Modeling

Example 3 (Maximum profit)

​A company produces two types of pots, X and Y, using copper and steel. A Type X pot requires 300 g of copper and 100 g of steel, while a Type Y pot requires 100 g of copper and 200 g of steel. The Type X pot yields a profit of Rs. 400, and the Type Y pot yields a profit of Rs. 500. Find the number of units of each type of pot that the company should produce with 5 kg of copper and 12 kg of steel to achieve maximum profit.

Mathematical Modeling

Example 3 (Maximum profit)

​A company produces two types of pots, X and Y, using copper and steel. A Type X pot requires 300 g of copper and 100 g of steel, while a Type Y pot requires 100 g of copper and 200 g of steel. The Type X pot yields a profit of Rs. 400, and the Type Y pot yields a profit of Rs. 500. Find the number of units of each type of pot that the company should produce with 5 kg of copper and 12 kg of steel to achieve maximum profit.

Multiple Choice

A municipality planning team in Pokhara is developing a model to predict traffic flow changes based on a new proposed highway. According to the text, this activity of describing a real-world problem in mathematical terms is best defined as

• Classical applied mathematics

• Pure mathematics

• Modeling

• Pedagogy

Multiple Choice

In the 'River crossing' puzzle (farmer, goat, wolf, cabbage), the text explains that different groups of pupils use counters, drawings, or computer programs. What common purpose do these different tools serve in this context?

• They are models used to assist student thinking

• They are methods for achieving maximum profit

• They are examples of pure mathematics

• They are all forms of calculus

Roots of modeling

1. ​Childhood Play

Roots of modeling

1. ​Childhood Play

2. Estimation and Error

Roots of modeling

1. ​Childhood Play

2. Estimation and Error

3. Diagrams and Mental Images

Multiple Choice

The text discusses the 'roots of modeling' as natural, spontaneous acts. Which of the following scenarios from a childhood in the hills of Nepal best exemplifies one of these roots?

• Following a teacher's instructions to solve a word problem from a textbook

• Using stones and twigs to build a small-scale model of their family home

• Learning the formal proof of the Pythagorean theorem

• Memorizing multiplication tables by chanting

The process of modeling