# Teacher Pedagogical Guides

Detailed teacher training materials that show you how you can deliver lessons that deeply connect with your students.

# TGPs

## Suggestions on how you can take the next step

Pedagogy is the art of practice and teaching. The digital revolution is transforming the way in which we work and live. The skills that will be most useful for youth in the rest of their lives and careers, are shifting with it. Teachers therefore need a way to constantly update themselves on the state of the art in pedagogy, and Teacher Pedagogical Guides offer them the key to that. The following video explains the tool in detail.

Download our example TPG: **Linear Algebra**

# A walk through a TPG

## In Depth Description

Step 1: Context

As an example of a TPG, we have a look at the topic Linear Equations, which is taught in Mathematics Form 1.

Before we go into the actual content and methods of teaching of the topic, we introduce how the topic is laid out in the syllabus. We can see the specific objectives the curriculum requires you to cover, and how many lessons are planned for this particular topic. We can also see a small text laying out the rest of the topic.

**MATHEMATICS > FORM 1 > LINEAR EQUATIONS**

According to the Kenyan Curriculum guide, Linear Equations is taught in 12 lessons, covering the following specific objectives:

– Linear equations in one unknown

– Simultaneous linear equation

– Formation and solution of linear equations in one and two unknowns from given real life situations

This guide presents to you approaches you can use to deliver the topic. The guide contains lesson plans and examples that you can use to effectively teach the topic.

This guide first helps you understand **WHY **the topic Linear Equations is taught at this level of mathematics education. It then follows by telling you **HOW** to go about teaching it. This comes from research all over the world as to the challenges in teaching the topic as well as best practices around teaching it. It then goes ahead to show you exactly **WHAT** to teach in the form of the 12 lesson plans tailored for each single daily lesson.

Step 2: WHY

The most important step when introducing a topic, is convincing students of WHY they need to learn. It all starts with why. When students are on board and it is clear to them that the content matter is relevant, they will be much more motivated to learn. We’ve seen promising examples of how this higher motivation in turn results in higher learning outcomes.

**WHY TEACH LINEAR EQUATIONS**

At this level, the correct teaching of Algebra in general is absolutely critical in the future ability of the students to understands and use Mathematics in their daily lives. Linear Equations is a branch of algebra that enables people to work out various scenarios in life that involve unknown quantities. For example:

*If a quarry pays 10 shillings for every stone loaded onto a lorry, how may stones does a worker need to load in order to earn 1,000 shillings? The number of stones is the unknown here.*

*If a bakery uses Ksh. 10,000 to bake 500 loaves of bread and sells each loaf of bread at Ksh. 40, how much profit will it make? The profit the bakery will make is the unknown here.*

*Nakuru is 200km away, how much time will it take to get there if we travel at an average speed of 60km/hour? The unknown quantity here is time.*

It is also possible that there are two unknown quantities in some instances. For example:

*A 50kg bag of fertilizer contains phosphate and nitrogen in the ratio of 2:1 for every kilo in the fertilizer bag. Each acre of land needs 3 bags of ferterlizer. How many kilos of phosphate and nitrogen do we therefore need in 10 acres of land? The unknown here are the quantities of phosphate and nitrogen required*

Students have a natural tendency to question everything. One of the roles of education is to quench that thirst.

Step 3: HOW

The next step is HOW. The “How” provides teachers with methods that can be used to deliver this topic in a meaningful and enjoyable way. The suggested methods are gathered from the minds and creativity of our content experts, and are heavily supported by quoted academic sources. They expose teachers to new ways in which content can be delivered. This enables teachers to learn on the job, while students are given the opportunity to really experience the topic first hand.

**HOW TO GO ABOUT TEACHING LINEAR EQUATIONS**

Up to this point in the curriculum, most of the mathematics students face is of the arithmetic type. Algebraic thinking is not introduced early enough and this contributes to the difficulties students face in learning algebra.

*Bodanskii (1991), in Russia, focused mainly on the development and solution of written equations to solve verbal problems. He found that ten-year-old students who were introduced to algebra problems and notation for equations from first grade (six- or seven-year-olds) performed significantly better than twelve- and thirteen-year-old students who only had access to algebra from age eleven.*

In order to effectively teach Algebra therefore, we must use foundational principles and approaches involving open ended verbal problems. Rather than only introduce them to equations, we should model real life activities into equations and such approaches help develop their algebraic thinking.

*Carpenter and Franke (2001) focus on algebraic thinking through children’s discussions on equations and inequalities. They show that young children, who participated in classroom activities that explore mathematical relations, can understand and explain that an equation such as a + b – b = a is true for any numbers a and b*

Once students are able to model real life open ended problems into equations, we should then introduce them to written algebraic equations together with the rules of algebra (addition, subtraction, multiplication etc) which will help them solve algebraic problems.

There’s an enormous pool of effective learning methods available.

Every lesson is an opportunity to meaningfully engage.

# Step 4: Lesson Plans

## The WHAT-section. Suggested lesson plans

The last and biggest part of the TPGs are the Lesson Plans. Projected on top of the government advised content, we created lesson plans for each of the suggested lessons in the curriculum. These lesson plans expose teachers to activities that follow new and creative ways of teaching a certain topic, and that truly connect with students.

__SUB-TOPIC: Equations involving one unknown __

**First Lesson (Simple equations involving whole numbers)**

Use this introductory lesson to remind them of algebraic expressions and some of the rules involved in working them out. Specifically, use the following approaches:

Show a simple equation such as 3x+4=10 and ask students to solve for x by making sure that they have x alone on one side of the equation.

– First step is to subtract 4 from both sides of the equation and this will leave us with 3x=6

– Ask students what the next step is, some of them will know that you are supposed to divide both sides by 3 while some will think that you subtract 3 from both sides. At this point you tell them that 3x means 3 multiplied by x and so to have only x on one side, we need to divide both sides by 3

– The above explanation will work for some students while it won’t work for some. In order to resolve this, introduce a word-related scenario explaining 3x=6. For example, tell them that three sweets cost 6 shillings, i.e 3x=Ksh.6. How much is one sweet? At this point, all of them should be able to know that one sweet is 2 shillings and they will be able to see that dividing both sides of the equation by 3 gives this answer.

Repeat the above process using a new equation of the same type e.g 2x+4=8 or even 4x-6=14. Ensure you create a word-related scenario to explain the final part of the problem as done above e.g 2x=4 could be two pens cost 4 shillings, how much does one pen cost? And 4x=20 could be 4 students sit on one desk and there are 20 students in the class, how many desks are there in the class?

__Student Practice__

Ask students to pair up and ask them to solve equations similar to the ones given to them. Give the equations one at a time and ask them to work them out, creating word-related scenarios for each of them.

Repeat with as many equations as possible, mixing addition and subtraction equations until time is up.

# Assessment

## Adapting lessons to student learning

What becomes apparent if we dive deeper into the proposed lesson plans, is that some contain assessments or revision. These assessments provide the teacher with insights into how their students are learning. Insights which are then used to steer the remainder of the lessons, to ensure all students are up-to-date with the curriculum.

To learn more, continue to our information page and video about Diagnostic Assessment.

Is your school ready to dive into the future? Let us know how we can help you!

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