K12 Van Hiele Math

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  HUNI_logo_en

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  How do Students learn Math?

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  The Van Hiele Theory of Geometric Thought

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  HUNI - K12 Van Hiele Math Evaluation Platform - Business model canvas

The problem “Van Hiele Math Evaluation Platform” solves

In the Republic of Croatia, apart from international research PISA (math) and TIMSS and already long attempts to research through national exams, no major research on students' mathematical achievements has been conducted.

In the Republic of Croatia, nobody has so far explored Bloom's or van Hiele's level of achievements in mathematics teaching, or it was sporadic! Through the action research NGO HUNI, Croatian association of teachers researchers (www.huni.hr), are problematizing the conditions of s educational activities by trying to devise, apply, and, explore suitable solutions. For a number of reasons, we have formed this project of Action research on the achievements of Croatian students.

In 2019. as the first year of Croatian students testing showed us that students' math knowledge in the concept of functions and concrete functions taught in school mathematics (linear, square, exponential) is below math knowledge in Van Hiele theory level.

Worrying results shows that only 3% of elementary K8 students knew how to solve a task appropriate to their age.

The project is focused on the teacher's determination and increase in student achievement levels in the basic concept of mathematics - in the concept of functions and concrete functions taught in school mathematics (linear, square, exponential, logarithmic, trigonometric). These functions are the basis of the use of mathematics in natural sciences (physics, biology, and chemistry). The function concept is closely related to computer science, computional thinking, and programming and as such a very important segment of information technology.

Bloom's taxonomy and van Hiele's theories prevailed in world science. A large number of surveys published professional and scientific articles, and doctoral dissertations suggest that the proposals of today's changes in mathematics teaching should be based on concrete conducted research of practitioners in action research. From a mathematical point of view, van Hiele's levels research gives much better insight into the mathematical achievements of students.

The image shows "How do students learn Math?"



With this project of teachers action research, we want to find out/spotlight/emerge van Hiele's level of student achievement in functions as a basic concept in Croatian school mathematics and offer improvements in teaching and learning through this project.

Croatian project short description is available @ https://www.huni.hr/wp-content/uploads/2020/04/HUNI-Van_Hiele_Project_short_04.2020-eng.pdf

How We built the solution

We initially explored at what level of knowledge are students in the Republic of Croatia according to Van Hiele's theory.

Computer technology, computers, and educational dynamic software enable all students of this level to learn the functions and their application. We have "incorporated" all of this into van Hiele's theoretical application of defining levels for functions which power lays in simplifying complex situations and predict results.

Van Hiele's theory is well-known and tested globally for geometric content levels in mathematics teaching from 1st grade to 8th grade. (These are K1-K8.) And these levels were explored at individual student ages.

For a better understanding of Van Hiele Theory applied in geometry thought and student's scaffolding in knowledge, representation is shown in the image "The Van Hiele Theory of Geometric Thought" - visualization description."



HUNI has defined beyond Van Hiele's level for elemental functions and is now exploring knowledge of these levels and for individual functions and according to age (K8-K12).

Particular attention was paid to Standard 8: Principles and Functions of K5-K8, which elaborates:

• describing, extending, analyzing and creating the rule of law;
• describing and displaying links to tables, graphs, and rules;
• analyze functional links to explain changes in results for different data entered;
• how to use the laws and features to display and troubleshoot problems.

In Standard 5: Algebra from K9-K12 elaborate:

• investigate situations containing variable sizes and present them with terms, equations, inequalities and matrices;
• use tables and graphs as a means of interpreting the terms equations, and inequalities;
• perform expressions and matrices operations and solve equations and inequalities;
• respect the power of mathematical abstraction and symbolism.

In Standard 6: Functions of K9-K12, the teaching of functions is elaborated:

• designing and analyzing relationships using tables, oral rules, equations, and graphs;
• switching between tabular, symbolic and graphical views;
• recognizing that many problem situations can be shaped by the same type of function;
• analyzing how parameter changes affect function graphs.

Exponential function test example: [https://www.huni.hr/wp-content/uploads/2019/11/Exponential-function-HUNI_engl1.pdf]

What We have done during the weekend

While lacking EU funding projects scheme for fundamental research, the necessity for international EU28+ recognition arise because of presents situation needs and future project deployment.

We made initial EIC and Mentors connection, start to build network connection, learn about EU\EIC platforms and financing opportunities, designed further project phases, build Project Business Model Canvas, and agree on other details.

Prepare the research projects’ first steps for the initial implementation outside Croatia.

The solution’s impact to the crisis

Although this project is not directly related only to the crises, but only emphasizes the necessity for having math evaluation and learning platform, which will guide student in learning, testing them, evaluate their knowledge, and help teachers to give recommendation what must be fixed in order for student to progress and achieve higher level of math knowledge.

What's next for K12 Van Hiele Math

Project Phases

1. Fundamental Research: by the end of 2020

A. Define our geometry tests and a new test for functions. Test students and investigate the situation in the Republic of Croatia in second testing wave in 2020.

Prepare initial project available for EU28+ student testing in 2020\2021:

• According to the results of solving the tasks and the experience of the teachers in this action research, tests (i.e. task examples) will be "standardized" in accordance with the van Hiele's levels and the age of students. In this way, it will be pointed out as transparent alignment and linkage of the achieved level with the class of mathematics. The aim is to implement van Hiele levels in Croatian (EU28+ states) math curriculum education (primary and secondary).

• After the action research activities, the achieved levels and experiences will be included in the van Hiele level Handbook for teachers, the students, and the parents and thereby will increase equalizing the level of assessment of the students themselves. The Handbook would enable other interested teachers to "try" themselves in the deliberation of solving problems in their classes (teaching and learning).

• Series of workshops on van Hiele levels will be organized for teachers and curriculum administration.

B. Create detailed action research project documentation, sketch technology phases, the team with the required skills to design the final solution, feasibility study.

C. The above phase is the Minimum Viable Product (MVP) that needs technological phases 2.&3.

2. Technology Research & Feasibility: 2021-2022

A. Formulating a technological concept

B. Experimental proof of concept (Blockchain)

C. Laboratory validation of the technological concept

3. Product\Platform Operational Design & Demonstration: 2023-2024

A. Technology validation in a relevant environment

B. Demonstration of technology in a relevant environment

C. Demonstration of technology in an operating environment

D. Established and qualified technical and business system

4. Market: 2024

Successfully proven technology

• “Van Hiele Math Evaluation Platform”, i.e. "recipes what after evaluating K12 math knowledge according to Van Hiele theory, needs to be fixed in student education", while monitoring of students’ learning process, a standard K12 mathematical tests.

• Since this is blue ocean project\product, without existing competition or easily replicable solutions, business opportunity spreads in the implementation on EU28 market sized of more than 30 million primary and more than 55 million secondary school students as target users within B2G\B2B (Government\Publishers & Edu institutions).

"K12 Van Hiele Math Evaluation Platform" - High level overview details can be found in Business model canvas.

NEEDS for HUNI Project phases 1.-3.:

Implementation of prepared "K12 Van Hiele Math Evaluation Platform" - Business model canvas

A. EU\EC\ESF\EIC\VC(preseed) - investment phases 1.-3.:

• Secure Investment for Fundamental Research Phase: 1.A., 1.B., 1.C.

• Secure Investment for Phases 2.&3.: Technology Research & Feasibility; Product\Platform Operational Design & Demonstration

B. EU+ Institutions\EC Activities for adoption initial research project within EU28+ member states with Ministries of Educations\Edu institutions

• Opportunity to run the initial test project in EU28+ countries for student math knowledge evaluation

• As replications of Project Van Hiele Croatia in EU28+ country with small investment; covering 15 schools (K12) and ~10.000 students

The value of Our “Van Hiele Math Evaluation Platform” after the crisis

As a standard for EU28+ K12 students’ mathematical evaluation, we aim to minimize the situation of students having difficulties in learning math because the Van Hiele Theory will be implemented in National math curriculum.