What is a list of math books
Learning math means reflecting on experiences
When parents compare today's textbook pages with their own earlier ones, questions and doubts often arise about the usefulness of assignment formats. How does this reflect a modern understanding of learning? We ask Joachim Becherer, math teacher and long-time school director, which findings shape the content of a modern textbook.
Children bring very different previous mathematical experience and knowledge to the class. This is a great challenge for teachers, educators, school principals and authors like you. Can a textbook meet these different requirements? Or to put it another way: does a textbook have to be able to do “everything” today?
Cups: Not everything, but a textbook must be able to do the right thing. It has to be conceptually oriented towards how learning works. The human brain is not designed to learn details. Rather, it learns rules and structures in contexts successfully and permanently. The learning consists e.g. B. not in the fact that a child knows hundreds of thousands of addition problems by heart and can call them up in the brain "from a drawer". Rather, a pool of relatively few tasks that have been mastered by heart is sufficient that can be used to develop other tasks in relation to them.
What connections should the children discover while arithmetic?
Cups: A child knows e.g. B. in the course of the first school year by heart that 4 + 3 = 7. What is decisive, however, is that it has also discovered, reflected on and learned the existing structures, we call them computational strategies. As a result, it can later derive 4 + 3 = 7 from the knowledge: 14 + 3 = 17, 40 + 30 = 70, 4000 + 3000 = 7000, but also 204 + 3 = 207 or 240 + 30 = 270 and much more. And another example, try it yourself: Find the next task in the task package: 66 - 38; 62-34; 58-30. As you can see from this pattern, these structures can be used on different levels. This means that we can also offer high-performing students an optimal offer for learning through discovery. We do not see “promoting and demanding” as different areas of requirement; Rather, correct encouragement means challenging everyone at their level of performance.
What else is beneficial for successful learning? How do you implement these considerations in textbooks?
Cups: To answer your question, it will help to take a look at the findings of current brain research. The more often and imaginative paths of thought with the same structures are followed, the more routinely these paths are used. I like to compare such a path of thought with a mountain meadow or scree field that has not been traversed before. If you walk over such an area only a few times, you will only see a trace at most. The grass stands up again and no trace is visible anymore. The more often you walk such a path, the faster it becomes a permanent trail, a narrow path, a wider, easier path to walk. But: If a path is not used for a long time, it will grow over again or it will be buried by the rubble.
It is important for all children in the learning process to walk the “paths” in a variety of ways and to talk about them. So we keep asking the children to describe their approach to each other. We cannot “hear” this in the book, but we add utterances in speech balloons as an example to initiate and support these processes. The rule is not "a lot helps a lot", but rather "the right thing helps a lot". If task packages with a good structure are created, the children reflect on them and discover important arithmetic strategies.
If you compare today's textbook pages with earlier ones, parents in particular have questions and doubts about the usefulness of task formats. Parents ask themselves, for example: "Why aren't there just arithmetic problems?" How do you see it?
Cups: In this context, I refer to two fundamental findings of brain research: “Learning is reflected experience” and “Children learn from suitable examples.” It is therefore the task of the textbook authors to offer teachers the appropriate impulse task formats for learning through discovery in the medium of textbooks and accompanying materials. If we succeed in using people's innate curiosity to shape the learning processes, we are on a promising path.
And one more thing at the end: It is therefore not enough, e.g. B. to keep an eye on the results of arithmetic tasks, rather the view must also be directed to the paths that led to the results.
Joachim Becherer, teacher for elementary, secondary and technical schools, long-time headmaster, active in teacher training, textbook author and editor, z. B. the new textbook "Jo-Jo Mathematics" (Cornelsen)
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