In today’s digitalised world, we are more and more used to drawing and calculating with the help of digital tools. Although digital tools for mathematics have the advantage of being quick and convenient, experts argue that doing things by hand can have an added cognitive value. Graphing functions by hand for instance, is a hands-on experience that can help the student better learn the basics of functions. 

Teacher Signe Reidla from Peetri Lasteaed-Põhikool (Peetri Kindergarten and Primary School) combines manual with digital work to complement each other. 

In this scenario, Signe Reidla addresses the topic of functions in the curriculum, with the following learning outcomes:

1.    Explain the meaning of proportional dependence based on real-life examples.

2.    Plot a function graph (both manually and digitally) and read the function and argument values from the graph.

3.    Explain (using computer-generated dynamic drawings) the dependence of the position and shape of the graph of the function on the coefficients in the expression of the function (in case of a quadratic function, only on the quadratic coefficient and the free member).

4.    Explain the meaning of zeroes and find them in the graph and formula.

5.    Read the parabolic peak from the figure and calculate its coordinates.

6.    Learning content: Variable size, function. Proportional and inverse dependency. 

7.    Do practical work: proportional and determining the inverse relationship (e.g.,    distance, time, speed) when moving. Linear function. Square function.

Firstly, she encourages independent learning by providing quizzes and interactive games to students. Secondly, she prepares the questions to give constructive feedback to incorrect answers. Thirdly, she checks student performance to decide whether she will give some students more individual work. Fourthly, she uses online surveys for self-assessment and rubrics for non-graded student assessments.

Students do a short test built with Quizalize as homework before coming to the class. While going through the test, students get instant feedback to their answers. For self-reflection, Signe asks the students to also review each other’s answers and analyse the results. Preparing these tasks is easy albeit a bit time consuming for the teacher. However, this material can always be reused in future classes.

To perform the in-class assignments, students are divided into groups using class123, a classroom behaviour management tool (Figure 1 and Figure 2).The teacher gives the students feedback in the same environment on the group work (points can be given to group members). 

Figure 1 class123 is a classroom behaviour management tool where you can reward good student behaviour and provide feedback.

Figure 2 Classroom groups can be randomly generated in the class123 tool.

The lesson consists of 6 different activities and a timer, which is also created with class123 (Figure 3), is used to determine the time for each activity.

Figure 3 Similar to ClassDojo, class123 also has classroom management features like timers.

The teacher provides explanations at the beginning of the lesson using the Nearpod environment. Group work is done based on this. Students also enter their answers on Nearpod The teacher should provide feedback at least for the answers that are most likely to be incorrect. This will give more time for the teacher to check on groups in person.

Figure 4 Teacher instructions for math problem delivered on Nearpod.

If the teacher does not want to use numerical grading, she can give feedback to the group and use private messages to give individual feedback on student performance and to provide guidance. 

Finally, using the GeoGebra program, students verify the accuracy of graph plotting and zeroing on their own. This is a good practice for self-assessment and independent learning.

Teacher Signe has prepared a short interactive game on Purposegames (example in Estonian). Students do this individually after the teamwork. It takes a few minutes to prepare the game, taken that one knows the environment and what they want to achieve. There are many assignments that have been prepared and can be loaded up for the students. The game is played for speed multiple times, until achieving 100% as score. This can take up to a few minutes. With this game the teacher can reinforce what the students have learnt and check if they have acquired the necessary knowledge during class.

Students assess their teamwork and learning outcomes on an online survey created on Proprofs (or any other survey tool). The survey asks students to assess their knowledge, but also how well they think they worked as a team (Figure 5). This is a great way to practice self-assessment, but also help the students reflect on their teamwork and see what could be improved next time.

The results can then be discussed briefly in teams and with the class. The results provide input to the teacher for putting together the necessary tasks for the next lesson. If some students seem like they need more practice, the teacher can also give them some additional individual homework. At the end, the teacher summarises the students' thoughts and concludes the lesson. 

Figure 5 Some survey items for self and group assessment created with the survey maker tool of Proprofs

Signe also creates an assessment rubric of student group work on forallrubrics, fills in the model and shares it with the students (Figure 6). The site is used throughout the year with students to keep track of their progress. It gives Signe a chance to make sure students understand how and why the teacher gives them certain feedback. It also helps the teacher feel that she has been fair to all students/groups, because each level in the model is thoroughly described. You can find instructions for using the tool in this video in English. 

This practice is followed by activities where students begin to use new knowledge to plot and study function graphs.

Figure 6 A sample rubric on the forallrubrics tool

This scenario can be implemented in a hybrid and blended context. For the group work students can work in mixed in-class and online groups, provided that the in-class students have access to technology and that the code to the Nearpod lesson is shared with all the students (even the manual drawing is done on an online drawing board within Nearpod). It would be very useful for students to be able to use a backchanneling app to discuss their work in groups. For partner activities that include peer assessment, a shared document would be suitable so that students can exchange their results and provide their peers with feedback. All the other activities require indivdiual work on a device, which can be done in both hybrid and blended settings.