Rubik's Cube as Mathematical Learning
A classroom project centered on pattern recognition, planning, algorithmic thinking, spatial reasoning, persistence, and comparing strategies.
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Mathematics educator · EdTech creator · author · project designer
Hélio Junior.
Hélio Junior.
Teaching mathematics. Designing ways to experience it.
A professional trajectory that connects classroom practice, teacher leadership, academic research, documented school projects, educational publishing, web learning, and Android products.
Since 1997 Mathematics educationICMC/USP Professional Master'sSchool + EdTech Classroom to digital learningBrazil → English International portfolio
Hélio JuniorMathematics Educator & EdTech Creator
Professional profile
Nearly three decades connecting mathematics, people, and learning experiences.
Hélio Junior is a Brazilian mathematics educator with higher-education qualifications in Mathematics Education and Pedagogy, and a Professional Master's degree in Mathematics from the University of São Paulo (ICMC/USP).
Teaching since 1997, his trajectory includes classroom teaching, mathematics coordination, teacher guidance, school-wide projects, academic research, educational publishing, and the design of digital learning experiences.
He founded HUB da Matemática, where classroom experience became visual mathematics, pathways, games, stories, challenges, exam preparation, assessment resources, mobile learning, and tools for students and teachers.
Selected work
Six projects that show the breadth of the portfolio.
Rather than presenting a long list of tools, this selection shows how the work moves across classroom projects, school documentation, academic research, and educational technology.
Mathematics in Action
Mathematics Week, Tangram, operations challenges, construction tasks, games, film, art, entrepreneurship, and activities across the school community.
See the evidence →Knowledge Olympics
Olimpíadas do Conhecimento: logic and reasoning challenges created as a social-engagement initiative and designed to connect learners through virtual competitions.
Explore the project →MATH NEWS
Two school newsletters translated into English, preserving documentary evidence of projects, student participation, activities, and educational context.
Open the publications →Educational Apps
ENEM, ETEC, and HUBMAT learning products show the move from instructional design to web and Android learning experiences.
See the apps →ICMC/USP Research
Professional Master's research investigating student learning, ENEM competencies, and flipped-classroom practices in Brazilian basic education.
Read about the research →Case study · Rubik's Cube
A puzzle became a laboratory for mathematical habits of mind.
The project began in 2011 during Hélio's school trajectory at Colégio Adventista UNASP-SP and continued in other educational settings. At EMEF Veremundo Toth, MATH NEWS records the project as an ongoing activity developed with students from 2019 onward.
The goal is not merely to solve the cube. Students observe patterns, anticipate consequences, organize sequences, revise failed attempts, compare strategies, and persist through a complex problem.
ObserveRecognize patterns and states
PlanAnticipate sequences and consequences
TestApply moves and evaluate results
ReviseLearn from unsuccessful paths
Inside a Mathematics Week
Evidence of mathematics happening across the school.
The MATH NEWS documents show a deliberately varied experience: mathematics appears through problems, physical construction, games, cultural references, communication, art, film, teamwork, and student production.
Poetry & filmMathematics discussed through language, reflection, and cultural experiences.
Tangram & geometryConstruction and spatial reasoning through geometric figures.
Four operationsStudents created strategies and discussed different approaches.
Spaghetti towerPlanning, structure, teamwork, testing, and revision.
Games & competitionsChess, checkers, OBMEP, logic, and problem-solving challenges.
Student productionArt, entrepreneurship, presentations, and school-community participation.
Reasoning, participation, and challenge
Two different projects use the idea of a learning challenge in different ways.
The international portfolio distinguishes the projects instead of merging them: the Knowledge Olympics is a virtual engagement initiative, while MatematicaToth was a school-based project with planned knowledge stations.
Knowledge Olympics
Olimpíadas do Conhecimento uses logic and reasoning challenges to stimulate participation and connect learners through virtual competitions.
View the Brazilian initiative ↗MatematicaToth Knowledge Stations
The 2024 MATH NEWS records a future-project plan for the Science and Technology Week with 16 knowledge stations designed for students to move through a sequence of mathematical experiences.
See the English record ↗Educational technology & apps
Instructional ideas translated into products for web and Android.
The role represented here includes concept development, educational architecture, content organization, learning-flow design, and product direction. Real product visuals are shown below.
Brazil · National examination preparation
HUBMAT ENEM
ENEM is Brazil's national high-school examination and an important route into higher education. The HUBMAT project organizes preparation by subject area, practice, review, and study direction.
Portfolio role: concept, instructional design, content architecture, and educational product development.
Open the Web Experience ↗Android / Google Play project
São Paulo · Technical-school entrance preparation
HUBMAT ETEC
ETECs are public technical schools in the state of São Paulo. The app uses previous-exam questions, study by area, review, progress tracking, and structured preparation for the entrance process.
Portfolio role: concept, instructional design, product architecture, content organization, and educational direction.
Mathematics learning · structured pathways
HUBMAT
A mathematics learning product built around exploration, practice, challenges, applications, progress, rewards, and student choice. Android and web access are offered as separate products.
Portfolio role: concept, learning architecture, curricular organization, experience design, and educational product direction.
Brazilian education context
A short guide for international readers.
Several projects come from Brazil. These terms are explained here so the evidence can be understood without prior knowledge of the Brazilian education system.
Brazil's National High School Examination, widely used in access to higher education.
Public technical schools maintained by the state of São Paulo, with a competitive entrance process.
The Brazilian Mathematics Olympiad for Public Schools, a national mathematics competition.
Youth and Adult Education, a Brazilian educational pathway for learners completing basic education later in life.
Professional timeline
Teaching, leadership, research, and creation.
The portfolio is organized chronologically so the digital work remains connected to the professional experience that preceded it.
Mathematics teaching begins
Classroom teaching, student follow-up, assessment, and the development of learning activities.
Mathematics coordination
Mathematics coordination in the Anglo educational system at Colégio Adventista de Santos, supporting the pedagogical work of the subject area.
Rubik's Cube Project
A school project begins and later continues in other educational contexts.
Professional Master's · ICMC/USP
Research on learning, ENEM skills and competencies, and flipped-classroom practices in basic education.
Teacher guidance in São Paulo
Work as a subject-area teacher leader in the municipal school network, supporting planning and mathematics teaching practices.
MATH NEWS & Mathematics in Action
School projects and student participation documented through two mathematics newsletters.
HUBMAT & HUBMATH EDUCATION
Educational technology, interactive mathematics, digital products, and an English-language learning portfolio.
Pedagogical method
See → Explore → Question → Practice → Explain → Apply
A recurring design logic connects the classroom projects, research, games, visual tools, pathways, and interactive labs.
01SeeMake structure visible.
02ExploreManipulate, compare, and notice patterns.
03QuestionTurn observation into a mathematical problem.
04PracticeBuild fluency without losing meaning.
05ExplainUse language to make reasoning explicit.
06ApplyTransfer ideas into new contexts.
Published academic research
Research connected to a practical question: how do students learn better?
In 2019, Hélio Junior defended a Professional Master's dissertation at the University of São Paulo (ICMC/USP) examining learning related to ENEM skills and competencies and the use of the flipped classroom in Brazilian basic education.
English rendering of the title: Analysis of Learning of ENEM Skills and Competencies through the Use of the Flipped Classroom in Basic Education.
The research supports a principle that remains visible in the later portfolio: technology is useful when it creates better conditions for students to investigate, practice, receive feedback, and make sense of ideas.
View the Dissertation at USP ↗2019 · ICMC/USP
Research themes
- Student learning
- Flipped-classroom practices
- ENEM competencies and skills
- Technology-supported learning
- Teaching innovation in basic education
The dissertation is hosted by the University of São Paulo in Portuguese.
Evidence & publications
Documents that allow the work to be inspected directly.
The portfolio links to primary evidence instead of relying only on descriptive claims.
MATH NEWS No. 1 — English editionMathematics Week · May 2023↗
MATH NEWS No. 2 — English editionMathematics in Action · June 2024↗
Professional Master's DissertationUniversity of São Paulo · ICMC/USP↗
HUBMAT ETEC on Google PlayPublished Android learning product↗
HUBMAT on Google PlayPublished Android mathematics-learning product↗
Selected educational products created in Brazil
Different doors into mathematics.
These Portuguese-language projects show additional directions in the broader HUBMAT body of work.
Visual thinkingVisual MathematicsModels and representationsGuided progressionMathematical PathwaysExplore, practice, and advancePlay & strategyMathematics GamesLogic, space, precision, decisionsDaily learningHUBMAT 5minShort, focused mathematics sessionsNarrative learningMathematical StoriesCharacters, situations, and ideasExperimentationMathematics SimulatorsTest ideas by changing variables
Schools · universities · educational partnerships
Interested in mathematics education, digital learning, or project collaboration?
The portfolio is open to professional conversations involving mathematics education, instructional design, digital learning resources, school projects, and educational partnerships.