Visualizing Mathematics With The MathBot

Author: Christina Todorova , Petar Sharkov , Ivaylo Gueorguiev , Pavel Varbanov , George Sharkov
Summary of the Activity Plan

The goal of this workshop is to introduce and exercise mathematical concepts, which are covered in the national school curriculum for mathematics for the fourth grade in Bulgarian schools, using programming and robotics. Participants play 5 different games with the robot. Every game builds on the previous one and is broken down into quests, through which they exercise their knowledge on mathematics and adopt new concepts while exercising them. Children program to make the robot move and they make the robot move to solve a mathematical problem. In addition, and of equal importance to the subject of mathematics, this workshop is specifically designed to support and encourage the development of problem-solving skills, communication, collaboration, flexibility and adaptability and digital fluency. Within the sessions, students are required to shift roles within their group, which consist of different responsibilities, aiming to ensure that flexibility and adaptability skills are fostered. During the second session, students are not reminded to shift roles, which encourages communication, as well as provides students the chance to fall back into the most comfortable role within their team. Robotics is intriguing and fun, which is why we believe it makes a wonderful tool, in addition to the general school curriculum, for learning mathematics. We know that learning by doing makes children fall in love with mathematics and robotics is the way we visualize mathematics.

Type of Activity: Workshop Curriculum Aligned: Partially aligned
Subject:
  • Maths
Curriculum and Country: This workshop is aligned to and specifically designed to support the Bulgarian national curriculum on Mathematics for the fourth grade.
Language: English
Domains
Science: 0
Business: 0
Technology: 5
Engineering: 0
Mathematics: 10
Arts: 0
Societal Issues: 0
Life Skills: 0
OBJECTIVES AND SKILLS

Subject Related:

- Measuring angles; Different types of triangles by length of sides (scalene, isosceles, equilateral) and by width of angles (acute, right, obtuse); Circles and the elements of a circle; Positive and negative number; Proportions;

Skills Learning Outcomes:

  • Students will exercise formulating and expressing ideas (collaboration and communication), curiosity, tinkering and experimentation (creativity and problem-solving), decision-making (collaboration and communication) and much more.
  • Skills to be fostered:

    • Collaboration
    • Creativity
    • Teamwork
    • Problem Solving
    ARTIFACTS

    Digital artifacts:

    Robotic artifacts:

    WHO? WHERE? HOW LONG?

    Gender: both

    Age Group: 8 - 11 Years

    Class Size: large

    (Ideal) Group Size: 4

    (Ideal) Grouping Suggestions: gender,ability

    Prior knowledge: Third-grade knowledge in mathematics, basic knowledge of the Scratch interface

    Special needs and abilities:

    Environment: hall,classroom,indoor

    Style of room: A spacious hall, with one computer and empty table per team, enough chairs, projector or smart TV screen, whiteboard and enough power plugs.

    Sessions: 2

    Session Duration: 4h00

    Total Duration: 8h00

    INTERACTIONS

    Actions:

    • Exchange ideas
    • Dialogue
    • Negotiation

    Relationships:

    • Collaborative

    Roles in the group:

    • Pre-defined roles
    • Emergent roles
    • Role exchange in the group

    Support by the tutor(s):

    • Intervene
    • Monitor
    • Facilitate
    TECHNOLOGY
    Technology Used:
    • Dash & Dot
    • Robotic Dreams
    • MOSS
    • LEGO Mindstorms

    Price per Kit: €51 - €100

    Technology Needed: Computers

    LEARNING AND TEACHING

    Teaching Methods:

    No Teaching Methods
    HOW TO
    INTRODUCTION & PRE-WORKSHOP EVALUATION
    Description: The tutors introduce themselves, explain what they do and why they came to the school. Children are asked about their attitude towards mathematics, whether they like it and whether they think robots are useful for teaching mathematics. The purpose is to become familiar with the audience and vice versa and to explore their existing attitudes. The researchers introduce themselves as robot enthusiasts and math-lovers and explain that in this workshop they will play and work together with the student teams in order to solve several mathematical games using the Finch robot. Tutors explain again the importance of feedback and student contributions which will be used to design even more interesting educational workshops. Following this, children fill out the Pre-Workshop Questionnaire evaluation activity. In case this is the first acquaintance with these students, they are asked to complete the Draw a Scientist evaluation activity. Children are provided with instructions on how to fill out the questionnaires. After the evaluation, the tutors continue the discussion about robots and ask questions about the parts of the robot. They introduce the Finch robot and ask children to fill out the “Parts of my Robot handout” together as a team. Afterwards, students are ready to refresh their memory on Mind Maps, by having to complete a group Mind Map on the abilities of their robot, based on what they know about the robot’s sensors. Following that, they are presented with the workshop rules. Every group is handed out a Mind Map with the workshop rules. The rules are explained and a focus is put on the importance of recording results, on protecting the robot and on switching roles within the team. Tutors try and emphasize to the students that in order to complete the task they need to collaborate with other students. The work of one person, no matter how good it is, is not going to be better than the collective work. Switching roles is of utmost experience to the success of the group and that everyone has to gain experience.
    Duration: 70 minutes
    Type: Introductory , Reflection , Evaluation
    Orchestration: Individual work
    Teaching Methods:
    Subject Related: Measuring angles; Different types of triangles by length of sides (scalene, isosceles, equilateral) and by width of angles (acute, right, obtuse); Circles and the elements of a circle; Positive and negative number; Proportions;
    Skills Learning Outcomes: Students will exercise formulating and expressing ideas (collaboration and communication), curiosity, tinkering and experimentation (creativity and problem-solving), decision-making (collaboration and communication) and much more.
    MOVING OUR ROBOT
    Description: Students implement their first programs that have programming blocks in a row. No loops or selection structures are needed. The first program should move the robot forwards. The robot is pre-assembled so students have to focus on programming and debugging their own programs. After a successful first program, they are asked to write additional code, so as to program their robots to move backwards, left, right, around its center (left and right) and create a stop button. Bonus games include making LED lights shine at a push of a button and change colors after another button is pressed. Students are programming the Finch robot developed by Birdbrain Technologies with the visual programming software Scratch. They are further showcased the difference between positive and negative numbers without going into theory, as programming the Finch to move backwards requires a negative value for the motors. Students understand that robots are programmable;
    Duration: 70 minutes
    Type: Exploration , Experimentation
    Orchestration: Group work
    Teaching Methods:
    Subject Related: Measuring angles; Different types of triangles by length of sides (scalene, isosceles, equilateral) and by width of angles (acute, right, obtuse); Circles and the elements of a circle; Positive and negative number; Proportions;
    Skills Learning Outcomes: Students will exercise formulating and expressing ideas (collaboration and communication), curiosity, tinkering and experimentation (creativity and problem-solving), decision-making (collaboration and communication) and much more.
    WAIT! AND DO A SEQUENCE OF ACTIONS
    Description: Students build on the knowledge, gained during the previous game to make a sequence of actions with the use of “wait”, to gain a smarter command of the robot. In this game, the robot has to complete a series of tasks on the push of a given button. Students apply sequences of actions to program their robot. Students are applying the skills and principles related to the argumentation and fostering of maker culture objectives, as well as the targeted skills from the social and action related objectives, similarly to Phase 2.
    Duration: 40 minutes
    Type: Exploration , Experimentation
    Orchestration: Group work
    Teaching Methods:
    Subject Related: Measuring angles; Different types of triangles by length of sides (scalene, isosceles, equilateral) and by width of angles (acute, right, obtuse); Circles and the elements of a circle; Positive and negative number; Proportions;
    Skills Learning Outcomes: Students will exercise formulating and expressing ideas (collaboration and communication), curiosity, tinkering and experimentation (creativity and problem-solving), decision-making (collaboration and communication) and much more.
    MATHEMATICAL GAMES – MEASUING LINES
    Description: Students attach a pencil to their robots using sticky papers. With a pencil they have to draw, by pressing only one button, lines with different values. They have to work with a ruler to make the measurements and have to do some precise coding to achieve their goal. This game requires students to discover fractions to achieve precise results. This game exercises proportional thinking and encourages experimentation. The second part of the game is devoted to applying arithmetical functions to achieve lines of a certain length. Students have to use fractions again, and learn or exercise their knowledge of calculating fractions. Students apply sequences of actions to program their robot and exercise arithmetical functions - multiplication addition, subtraction and division by including them as part of the games. They use measuring tools to complete the game (ruler) and test out in practice work with whole numbers and decimal numbers (without going into theory) by having to program the “wait time” to achieve precision with their results;
    Duration: 60 minutes
    Type: Exploration , Experimentation
    Orchestration: Group work
    Teaching Methods:
    Subject Related: Measuring angles; Different types of triangles by length of sides (scalene, isosceles, equilateral) and by width of angles (acute, right, obtuse); Circles and the elements of a circle; Positive and negative number; Proportions;
    Skills Learning Outcomes: Students will exercise formulating and expressing ideas (collaboration and communication), curiosity, tinkering and experimentation (creativity and problem-solving), decision-making (collaboration and communication) and much more.
    MATHEMATICAL GAMES – MEASUING ANGLES
    Description: As usually this game is conducted during the second session, students are given a simple task to perform within 10-15 minutes to refresh their knowledge on Scratch programming from the previous session. When they’ve done that, tutors engage the students in brief discussions about different types of triangles by length of sides (scalene, isosceles, equilateral) and by width of angles (acute, right, obtuse) to enable them to learn from one another. Building on their knowledge about angles, children are briefed on how to measure angles by the tutors. This is explained by one of the tutors and to reinforce the knowledge of the students, a handout with various figures is given out to the children to complete in groups. After making sure that each group feels comfortable measuring angles, we continue with a game, aiming to make children exercise what they know about angles. For this activity, children are given paper, pencils, colored markers and a protractor. They have to make the Finch turn around one wheel at speed 30. Students measure how far the Finch turns for different wait times, and they you use this information to figure out how to calculate the wait time for a particular angle, which is included in the bonus games.
    Duration: 80 minutes
    Type: Exploration , Experimentation
    Orchestration: Group work
    Teaching Methods:
    Subject Related: Measuring angles; Different types of triangles by length of sides (scalene, isosceles, equilateral) and by width of angles (acute, right, obtuse); Circles and the elements of a circle; Positive and negative number; Proportions;
    Skills Learning Outcomes: Students will exercise formulating and expressing ideas (collaboration and communication), curiosity, tinkering and experimentation (creativity and problem-solving), decision-making (collaboration and communication) and much more.
    MATHEMATICAL GAMES - CIRCLES
    Description: Students are engaged in a discussion about their knowledge on circles. Students come up with definitions about a circle and its elements. By doing this, children are encouraged to learn from one another and exercises their ability to express themselves and articulate complex concepts verbally. Afterwards, a game exercising knowledge on circles is explained. Students have to program the robot to draw a perfect circle by making it turn around one of its wheels for certain time. They have to experiment to find the precise value and have to collaborate with one another in order to test out various ideas. At this point of the workshop, they are no longer reminded to shift roles in order to observe if groups created a habit of social and team flexibility or team members naturally fall into a role that feels most comfortable. Following the first quest of this game, students have to program a robot to make a series of circles, a series of semi-circles. They are encouraged to draw out different elements of the circles, such as radius and diameter and measure them. This last game ends with a quest, aiming to exercise everything learnt by this moment – a complex sequence of tasks, including measuring lines and angles, drawing circles, making LED lights shine with different color every time the robot changes its direction of movement.
    Duration: 80 minutes
    Type: Exploration , Experimentation
    Orchestration: Group work
    Teaching Methods:
    Subject Related: Measuring angles; Different types of triangles by length of sides (scalene, isosceles, equilateral) and by width of angles (acute, right, obtuse); Circles and the elements of a circle; Positive and negative number; Proportions;
    Skills Learning Outcomes: Students will exercise formulating and expressing ideas (collaboration and communication), curiosity, tinkering and experimentation (creativity and problem-solving), decision-making (collaboration and communication) and much more.
    FEEDBACK AND EVALUATION, FINAL GAMES AND CONCLUSIONS
    Description: In addition to the activity sheets that students complete during activity phases, finally they discuss in classroom the difficulties, the different solutions, the limitations that may have found in every step. They also fill in an evaluation questionnaire and teacher gets short informal open interviews from students that want to share their experience. Children are asked about their recommendations and their favorite games from both sessions. Tutors give instructions on how to complete the evaluation papers and thanks children for participating in the workshop. Students have time for their final experiments. They are left with the opportunity to ask questions, test out different speeds and play Finch football. Finch football is a game, in which children are provided with a ball that the Finch has to “kick” into a gate, created by the team (with their hands or using anything they could find in the classroom). For this purpose, students have to write a sequence of action, executable with the press of one button. They can also play Finch pong, using the robot’s accelerometer and a pre-made program.
    Duration: 80 minutes
    Type: Exploration , Experimentation
    Orchestration: Group work
    Teaching Methods:
    Subject Related: Measuring angles; Different types of triangles by length of sides (scalene, isosceles, equilateral) and by width of angles (acute, right, obtuse); Circles and the elements of a circle; Positive and negative number; Proportions;
    Skills Learning Outcomes: Students will exercise formulating and expressing ideas (collaboration and communication), curiosity, tinkering and experimentation (creativity and problem-solving), decision-making (collaboration and communication) and much more.
    ASSESSMENTS

    INTRODUCTION & PRE-WORKSHOP EVALUATION: The tutors introduce themselves, explain what they do and why they came to the school. Children are asked about their attitude towards mathematics, whether they like it and whether they think robots are useful for teaching mathematics. The purpose is to become familiar with the audience and vice versa and to explore their existing attitudes. The researchers introduce themselves as robot enthusiasts and math-lovers and explain that in this workshop they will play and work together with the student teams in order to solve several mathematical games using the Finch robot. Tutors explain again the importance of feedback and student contributions which will be used to design even more interesting educational workshops. Following this, children fill out the Pre-Workshop Questionnaire evaluation activity. In case this is the first acquaintance with these students, they are asked to complete the Draw a Scientist evaluation activity. Children are provided with instructions on how to fill out the questionnaires. After the evaluation, the tutors continue the discussion about robots and ask questions about the parts of the robot. They introduce the Finch robot and ask children to fill out the “Parts of my Robot handout” together as a team. Afterwards, students are ready to refresh their memory on Mind Maps, by having to complete a group Mind Map on the abilities of their robot, based on what they know about the robot’s sensors. Following that, they are presented with the workshop rules. Every group is handed out a Mind Map with the workshop rules. The rules are explained and a focus is put on the importance of recording results, on protecting the robot and on switching roles within the team. Tutors try and emphasize to the students that in order to complete the task they need to collaborate with other students. The work of one person, no matter how good it is, is not going to be better than the collective work. Switching roles is of utmost experience to the success of the group and that everyone has to gain experience.

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    Author: Christina Todorova
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