cat3https://www.scientix.eu/it/c/message_boards/find_category?p_l_id=588349&mbCategoryId=02024-08-15T21:43:07Z2024-08-15T21:43:07ZRE: Share your classroom ideas hereTadeja Kobalhttps://www.scientix.eu/it/c/message_boards/find_message?p_l_id=588349&messageId=6026142017-04-25T19:13:01Z2017-04-25T19:13:01ZHello,<br /><br />I'm Tadeja. I teach math in a secondary school -young from 15 to 19 years. Here is my idea about using The number devil:<br /><br />When you teach a mathematical proof technique of mathematical induction, you can use the 6th chapter of THE NUMBER DEVIL. You can tell the students to find a property of Fibonacci sequence in the book which they can prove with induction.<br />I expect students to find the property: f(1)+f(2)+…+f(n)+1=f(n+2) from the book. Their task is:<br /><ul><li>to write this characteristic (by themselves) and</li><li>to prove it with induction.</li></ul>The proof is easy enough fort he 18 years students of secondary school. Later, when students have already done the task, teacher can assure if they have really understood the induction by asking them:<br />In the prove we use the iductive step:<br />f(1)+f(2)+…+f(n)+f(n+1)+1 =( f(1)+f(2)+…+f(n) ) +f(n+1)+1 = f(n+2) – 1 + f(n+1) + 1 = …<br />One can see that -1+1 =0, but this part could also work if we would use any other number instead of 1, let say 5. Why this is not right?<br />By asking students that question we check if they have understood the meaning of the base case and the whole proof technique.Tadeja Kobal2017-04-25T19:13:01Z