### Testimonials

Read what the acknowledged professors are saying about Paths to Math.

“Paths to Math” is an innovative, challenging and student centered method to teach and learn mathematics for lower-secondary and middle school students. Math is a universal language. This is the language that unites us all. Learning math is learning this language. To pave the way for a fascinating “Paths to Math” Maarit Rossi and Cecilia Villabona have developed an innovative strategic series of paths to make the life of teachers and students alike simpler and more productive towards math learning.

Their new method and Paths to Math are based on a ten-year research work of two teachers of matheducation in Finland, Katri Espo and Maarit Rossi. Espo and Rossi have put together a series of nine books that cover the entire Finnish math education curriculum for grades 7 to 9 or 10 (lower secondary or middle schools). The books are ahead of their time. They are constructed and written in a way that will develop the skills of children so they are ready for life, they think critically and they solve real life problems.

These pedagogical and constructivist ideas are at the heart of the questions used on international assessments such as PISA (Program for the International Student Assessment developed by the OECD to test 15 years old children in math, reading, problem solving and science). Paths to Math is based on a modern pedagogy of learning by doing and learning by thinking, of learning to solve problems and learning to apply theory to real-life problems, situations or events. Paths to Math, therefore, is organized in ways that teachers and students can construct their own path with different levels of difficulties and speeds of learning; is thought as a fundamental tool to develop competencies but also to increase knowledge.

“Paths to Math” is a powerful pedagogical tool for teachers because it will allow them to tailor different paths or ways to teacher and learn math for every single student and for the whole class. Maarit Rossi and Cecilia Villabona have worked hard the last two years to update the 10-year project; to align it to the U.S. Curriculum and standards, to enhance it in ways that fulfill the PISA purpose of educating children so they develop the competencies and knowledge of students from around the world when they are at the end of their compulsory-basic education or at the beginning of their upper secondary or vocational studies.

Paths to Math is an innovative and interesting solution to produce a new kind of materials for the learning and teaching of mathematics. The materials are based on modern views of learning and draw versatility on the latest research concerning mathematics learning. The problems designed for students arise from themes they find interesting and are embedded in familiar contexts. In school settings they will undoubtedly – better than the traditional textbook exercises – motivate students to delve into mathematical problems.

Paths to Math draws on recent research literature on pedagogical principles for cognitive learning, motivational development, and related support by means of instruction, and brings these principles in a new way into daily school life. The materials designed by Maarit Rossi , Katri Espo, Cecilia Villabona and Jenni Stout also concretise, at the level of student working, such objectives that are seen important in PISA assessments, for instance, when it comes to responding to the competency demands of society, working life and further education in the future. By its innovative solutions, Paths to Math shows how the reformative needs arising from research and societal development can be taken to daily classroom activities. This type of new tools are necessary in order that the needs of change recognised at the level of theory can be Implemented in schools and eventually generate learning of a new kind.

I have had a chance to follow the work on the Paths to Math materials for quite a long time already, especially through Maarit Rossi’s long-term development work. I am convinced that the Paths to Math scheme successfully combines theoretical understanding of recent learning research and changed competency demands in society so that it will generate new innovations and deeper understanding of the interaction between teachers and students in daily school life. Hence, Paths to Math can serve as a very useful and pedagogically productive tool at school with regard to accomplishing the desired improvements in learning outcomes.

Statement regarding “PathsToMath“ by Maarit Rossi, Katri Espo, Cecilia Villabona and Jenni Stout.

The internet address https://pathstomath.com is a practical platform for an innovative teacher to plan different learning routes according to her students’ needs. The Internet offers much more application capabilities to a teacher to organize her classroom teaching.

The material is based on the up-to-date pedagogical solutions, i.a. development of thinking, learning by doing, skills of problem solving, problem posing and solving real-life problems. The material in PathsToMath is very much PISA (Program for International Student’s Assessment) type, since it forces learners to use their prior knowledge, instead of only to copy and imitate some teacher-given models. Every learner is an individual, and the Internet material gives to teachers opportunities to construct every student’s own learning path.

More than 15 years I have followed very closely Maarit Rossi’s and Katri Espo’s developmental work on the mathematics textbook series for middle school. The first version of the book was in Finnish with the name “Matka matematiikkaan“ [A journey to Mathematics] published 1996 by a Finnish publishing house Edita (Helsinki). The book series consisted of a theory book, nine learning guides and teachers’ material.

The textbook mentioned was very up-to-date in the middle of the 1990’s, perhaps a little too modern. But now our implementation of school mathematics teaching has developed so far that it is proper for our system. In the beginning of the 1990’s we wrote a booklet (Halinen & al. 1991) on the direction of Finnish mathematics teaching in that decade. Rossi’s and Espo’s book series implemented the ideas of the Halinen & al. booklet. Later on in the 2000’s we could compare our published ideas with those of the PISA agenda, and saw that our booklet was written in the PISA spirit, even before PISA comparisons. Thus I can state that Rossi’s and Espo’s book implemented very nicely the PISA requirements.

PathsToMath is an internet update of the book with cultural adaptation by Cecilia Villabona and Jenni Stout. It has been enhanced with interactive student materials,students videos and teacher videos, all available in the internet.

Soon to be translated into Spanish

Summarizing, I see Paths To Math as a powerful tool to develop mathematics learning in every country.