It is more than 13 years ago since I started studying mathematics at the University, but I can still remember what a professor told us beginners at the start of our studies. He said that we were going to have

## Are tests necessary? Part 9 – Final results

This year my students in grade seven have not had any standard tests. The reasons for this can be read in part 1 and how they are graded can be read in part 2. I wish that you take the

## Are tests necessary? Part 8 – Results(2)

Short recap: This year my students in grade 7 have had no standard tests. Instead, they are graded based on their performance during lessons. The idea behind all of this is that I want my students to develop competences that

## Are tests necessary? Part 7 – Results(1)

Before we start, if you have not read part 1 in this series, I do recommend you to do so before reading about the results presented in this post, in order to understand them. Here is a quick re-cap anyway:

## Using digital teaching material is only positive

During the last few years, digitalization in teaching has escalated and at the same time the discussion about the topic has also increased. However, discussions on the use of technology for teaching purposes have often had a negative tone in

## Are tests necessary? Part 6 – Midterm checkpoint

It has now been over three months since me and my students have worked together. During this period their mathematical skills have improved drastically. If the students would realize this for themselves, this would greatly improve their confidence in their

## Are tests necessary? Part 5 – Visible learning

If the learning process is visible for students it is proven that this will improve their results, but what is visible learning? The idea of visible learning is to make students take responsibility for their learning by making them realize

## Are tests necessary? Part 4 – Types of Matrices

During last summer when I planned out what I wanted to discuss in this series of “Are tests necessary” this topic was not included, so to me this feels like a small spin-off post. However, in part 1 of this

## Are tests necessary? Part 3 – Digital tests

I am going to start off this post by answering the question whether tests are necessary or not. My answer is yes. Tests are extremely helpful in gathering information about students progress for both the students and the teacher. However,

## Are tests necessary? Part 2 – Grading without tests

Since I am only going to grade my students based entirely on lesson activity, it has to be crystal clear for these students how the grading works. It will also be important for the students to be aware of how

## Are tests necessary? Part 1 – Introduction

According to recent studies, students in Europe do not do as well as they used to and the interest for scientific subjects is low. One example from Finland is that in 2016 there were half an applicant for every degree

## A modernised way to go through examples

After introducing a new topic in mathematics examples are needed to demonstrate how things work, especially in algebra since algebra requires a perfect understanding and there are many details to learn. Traditionally the teacher shows a few examples and discuss

## Discover variables

The normal reaction from students, when being introduced to variables, is asking “why do we need letters? Letters only make things more complicated”. If students have this attitude, it might be difficult to convince them otherwise. One way to get past

## Guide and assess student activity

I think it is safe to say that a synonym for “mathematics” would be “problem solving”. In one form or another you always solve problems whether it is simplifying expressions, solving equations or deriving proofs. When you are solving problems

## Focus on learning and not the grades

There is an obsession with grades in schools today. Not only from students but also from teachers. Many students are given clear instructions on what to accomplish and what tasks to do in order to get a specific grade. If

## Presenting a problem just beyond the scope of students’ knowledge

It is said that a teacher, teaching according to the student-centered model, should be someone who introduces problems just beyond the scope of students’ knowledge. Students are then to solve these problems, however they find fit, using many different sources.

## Tasks with different levels of difficulty – useful or not?

You do not have to be a master psychologist to understand that if you tell a teenager that he may choose from tasks with different levels of difficulty many teenagers will choose the easiest ones. Already from this point we

## The view on digital teaching materials

The digitization of schools is in full swing, and currently there are active ongoing discussions about how the digital teaching materials should be designed to function in the modern classroom. It is said that digital teaching materials in mathematics should

## Student-centered teaching in practice

Mathematics has always been seen as a theoretical subject. This is probably the biggest reason why a teacher always explaines new theory before students start practicing. To me and many others, mathematics is a practical subject. It is possible to

## The modern math classroom

What equipment should the modern math classroom have? Since most schools have had teacher-centered education the focus has been on what equipment the teacher should have. A good example of this is buying expensive smartboards for science classrooms. The price

## How much homework should students get?

As a new teacher you often wonder how much homework you should give your students. Even though the appropriate amount of homework is kind of important it is not the quantity of homework that is the important question. The question