On April 19 and 12 at 8: 00 am, Deng Yonggang, director of the Training Center of China Academy of Educational Sciences, lecturer Yu Hao and Lin Jianjun, deputy stationmaster of Jiangxi Equipment Station, accompanied by relevant leaders of Jingdezhen Education Bureau, Audio-visual Education Museum, leping city Education and Sports Bureau and Audio-visual Education Station, went to leping city No.9 Primary School to carry out the "Thirteenth Five-Year Plan" project on national educational science.
During this period, Min Xu, a teacher from Leping No.7 Middle School, taught a demonstration class-"Choosing a position with wisdom". Yu Hao, a lecturer, commented that the classroom of educational equipment should not only focus on "playing" and "solving", but also focus on "thinking". Let children experience thinking stimulation, train instant judgment ability, improve logical reasoning ability, form recursive iterative thought, establish mathematical modeling consciousness, explore minimalist model and experience modeling method.
Director Deng Yonggang emphasized that the focus of solving puzzles is human thinking, and students should fully experience the stimulation of thinking and think deeply. Teachers should innovate ideas, fully experience thinking difficulties, promote classroom formation and enhance professional development. Lin Jianjun, deputy stationmaster of the provincial equipment station, pointed out that teachers should creatively carry out research to promote children's thinking and intellectual development and cultivate follow-up talents for social development.
Inspired by the exhibition class "Taking the Throne by Wisdom" and expert comments, I became interested in taking the throne by wisdom, conducted some in-depth research, and gave this class to the children, so that I could hear their voices of thinking and growth while playing and having fun.
Taking the throne by intelligence is a puzzle game. There are eleven chess pieces in a row of wooden troughs, and the last one is red. The rules of the game are: two people take turns to walk the pieces, and each time they walk 1 ~ 2 pieces. Whoever can get the last red piece-the "throne" will win.
At first glance, it seems to be related to luck. In fact, it contains mysteries and rules to follow. May wish to guide students from less to more, step by step, and explore the laws contained in it.
First, guide students to understand that the rules of the game are: 1. Two people take turns to take chess pieces; 2. Take 1 ~ 2 capsules each time; 3. Take the last one to win.
Secondly, lead students to go deep into the game, experience it deeply, ponder it over and over again, and explore the inside story.
Lead the children, bit by bit, step by step, thinking while playing. It is not difficult to find that when there is one or two pieces, the person who takes them first will definitely win. When the number of pieces is three, the last player wins. There are two strategies: first, the first winner takes one, and the second winner wins with two, that is, 1+2 type; Second, the first winner gets two, and the last winner gets one, which means typing 2+ 1.
At this time, let the students operate and experience repeatedly: when there are only one or two pieces, the one who takes the piece first wins; When there are three pieces, the one who takes the piece later wins.
Subsequently, flags were added. Question: When there are four flags, which one wins, the first one or the last one? Let the students practice the operation, experience it in the operation and draw a conclusion: the first winner takes one, and then there are three left. At this time, the last winner is the first winner of this competition. The key is to win one first to ensure victory. Take two and lose. Similarly, when there are five pieces, it can be concluded that the first piece has taken two pieces, and then there are three pieces left. At this time, the last one, that is, the first one in this competition, won. The key is to win with two. Take one and you lose. The difference between these two strategies lies in whether the first one takes one or two for the first time. In fact, the purpose is the same, and there are still three left. When there are three pieces left, it will be clear who wins and who loses. After such practice, it can be concluded that when there are four or five pieces, the one who takes the pieces first wins.
After the experiment, when there are six pieces. Ask the students to repeat the operation in groups and realize that the latter will win in the operation. There are also two strategies: first, the first one takes one, the last one takes two, the remaining three, and the strategy of repeating three wins; Second, the first one takes two, the last one takes one, the remaining three, and the strategy of repeating three wins.
By analogy, step by step, let students guess whether the first player wins or the last player wins when there are seven, eight or nine pieces, and then verify and understand.
Finally, let the students go through one, two, three, four, five, six, seven, eight and nine blocks. The situation is the same, but it is reproduced or repeated.
In fact, the core of this game is the strategy of holding children when the three flags are hoisted. That is to say, this game has an essential minimalist mode-it can be divisible by 3. When the divisor is 3, all nonzero natural numbers are divided into remainder 1 number, remainder 2 number and divisible number. If you want to win, you must try to take the remainder of 1, and never take the divisible number. The remainder of 2 is the adjustment number.
In this way, no matter whether there are 1 1 or additional pieces, if one side doesn't know the inside story, the one who knows the inside story will definitely wait for an opportunity to win.
The rules of the game are made by people. Once the rules of the game are changed, it is necessary to re-explore the game strategy. If it is stipulated that you can take one, two or three at a time, how can you win?
At this time, students can be guided to use the same inquiry methods and strategies to explore.
When the number of pieces is 1∽3, the first player wins, and when there are four pieces, the last player wins. The strategies are:1+3,2+2,3+1. When there are five pieces, the first player wins. The strategies are: 1+ 1+3, 1+2+2, 1+3+ 1. In fact, the first receiver takes a piece first, and then the last receiver (that is, the first receiver in this competition) wins when it becomes four pieces.
Similarly, when there are six pieces, the one who takes them first wins. The strategies are: 2+ 1+3, 2+2+2, 2+3+ 1 In fact, the first winner takes two flags first, and the last winner (that is, the first winner in this competition) turns into four flags and wins.
When seven pieces are played, the first player wins. The strategies are: 3+ 1+3, 3+2+2, 3+3+ 1. In fact, the first winner takes three flags first, and when it becomes four flags, the last winner (that is, the first winner in this competition) wins.
When there are eight pieces, the last piece wins, and the strategy is to use it twice according to the strategy of four pieces.
Similar to the game mentioned in the previous paragraph, the core of this game is the strategy of taking children when four pieces are played. That is to say, this game has an essential minimalist mode-it can be divisible by 4. When the divisor is 4, all nonzero natural numbers are divided into remainder 1 number, remainder 2 number, remainder 3 number and divisible number. If you want to win, you must try to take the remainder of 1, and never take the divisible number. The remainder of 2 and 3 is the adjustment number.
When students have a thorough understanding, the rules of the game can be further changed. Through experiments, analysis and reasoning, a broader and more universal model can be obtained.
The rules of the game are: two people take turns to walk the pieces, and each time they walk 1~n pieces. Whoever can get the last red flag-"Throne" will win.
Winning strategy: the minimalist mode of this game-divisible by n+ 1 When the divisor is n+ 1, all non-zero natural numbers are divided into remainder 1, remainder 2, remainder 3 ... remainder n and divisible number. If you want to win, you must try to take the remainder 1, and never take the divisible number. Remainder 2, remainder 3 ... remainder n is the adjustment number.