A shift in mathematics education is underway in Germany, as the state of Lower Saxony prepares to delay teaching traditional long division until secondary school. The decision, set to take effect in 2027, prioritizes a deeper understanding of the concept of division over rote memorization of procedures.
How Traditional Long Division Works
Traditional long division, as illustrated by the example of 3,240 divided by 5, involves a step-by-step process of estimating how many times the divisor fits into portions of the dividend. This includes subtracting multiples of the divisor and carrying down remainders until the calculation is complete, ultimately resulting in an answer of 648.
The Alternative: Halving Division
The alternative method, known as halving division, breaks down the dividend into its component parts – thousands, hundreds, and tens – and calculates partial quotients separately. Using the same example (3,240:5), students would determine how many times 5 goes into 3,000 (600 times), 200 (40 times), and 40 (8 times), then add those results together to arrive at the same answer of 648.
According to Professor Timo Leuders of Freiberg Pedagogical University, the focus should be on conceptual understanding. He stated, “The important thing about dividing is not fast and safe calculation. The important thing about dividing is that you understand when you divide, why you divide, what it means and always deal correctly with division in different situations. And that is always promoted with the halving method.”
Shifting Priorities and Tool Use
Professor Leuders also dismissed concerns that learning the halving method would disadvantage students as they progress to higher education. He noted that traditional long division is “in the vast majority of situations” no longer required, as calculators are typically available from the 6th or 7th grade onwards, even for more complex calculations like dividing a seven-digit number by a three-digit number.
Regional Differences
While Lower Saxony is embracing the halving method, the state of Saxony intends to continue teaching traditional long division in primary schools. Saxony’s Minister of Education, Conrad Clemens, stated that the method will remain a learning objective in the mathematics curriculum for elementary students.
What Happens Next?
It is possible that other German states may consider adopting similar changes to their mathematics curricula, potentially leading to a more standardized approach to teaching division across the country. It is also likely that educators will continue to debate the merits of each method, and the long-term impact of this change on student performance remains to be seen.
Frequently Asked Questions
What is the halving method of division?
Beim halbschriftlichen Dividieren wird die Ausgangszahl, der Dividend, in mehrere Teilzahlen zerlegt und das Ergebnis in mehreren Teilrechnungen erlangt.
When will Lower Saxony begin delaying the teaching of traditional long division?
Das niedersächsische Kultusministerium hat beschlossen, ab 2027 das schriftliche Dividieren erst ab der Sekundarstufe zu lehren.
What does Professor Leuders say is the most important aspect of learning division?
Leuders erklärt: “Das Wichtige am Dividieren ist ja nicht das schnelle und sichere Rechnen. Das Wichtige am Dividieren ist, dass man versteht, wann man dividiert, warum man dividiert, was es bedeutet und immer in verschiedenen Situationen mit der Division korrekt umgeht.”
How might a focus on understanding the *concept* of division, rather than the mechanics, better prepare students for real-world mathematical challenges?