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  1. Free, Online Math Games | Math Playground
  2. Have a Blast Mastering Math Concepts
About Project Euler

Taylor correctly traces back the problem to syncopation : using symbols as mere abbreviations words, without calculation rules for putting them to work. One should not be too hasty in blaming them: even the best textbooks on formal logic present symbolic reasoning only at the beginning, and not in a form that is suitable for practical use in the remainder, let alone for the everyday practice of "working mathematicians" and engineers.

There is no other reason why logic textbooks abandon symbolic reasoning in later chapters and treat the remaining topics axiomatic set theory, ordinal numbers and so on with arguments in words.

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In brief, the title of Gries's paper The Need for Education in Useful Formal Logic appropriately reflects the state of affairs until shortly before its publication in in Calculational reasoning In the cited paper , Gries advocates calculational reasoning. This means that logical arguments are presented as symbolic calculations, stepping from one equation to the next using appropriate rules, and linking them by in equalities.

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As mentioned in the introduction, this is the convenient style mathematicians are accustomed to in algebra and calculus, but now extended to logic. For the purpose of formal reasoning by humans , it has turned out to be vastly superior to what is misleadingly called "natural reasoning". For its mechanization, additional work is needed. Many researchers and educators in Computer Science have been first experimenting and then, after inevitably becoming enthusiastic, systematically working with calculational reasoning.

Dijkstra explains How Computing Science created a new mathematical style. This is largely due to calculational reasoning Under the spell of Leibniz's dream pp. This idea is also advocated by Hilbert, who adds the following comment in his famous lecture Mathematical Problems at the International Congress of Mathematicians in It is an error to believe that rigor in the proof is the enemy of simplicity. On the contrary we find it confirmed by numerous examples that the rigorous method is at the same time the simpler and the more easily comprehended.

The very effort for rigor forces us to find out simpler methods of proof. It also frequently leads the way to methods which are more capable of development than the old methods of less rigor. In retrospect, when these ideas were put forward by Leibniz and Hilbert, the time was not yet ripe for their implementation in everyday mathematical practice, due to the aforementioned practical deficiencies in formal logic, also described in more detail in Gries's paper. Nowadays, however, due to the work of Dijkstra, Gries and others, it has become commonplace in the approach to Computing Science by many researchers and educators.

Funmath extends these advantages to mathematics for all areas of engineering. Design of Funmath As seen from the preceding discussion, a widely applicable formalism should be a free of defects and b support formal reasoning, i. Point b is the main criterion whereas a , being a necessary condition, is just a consequence. Various researchers including Dijkstra and Gries were so dissatisfied with the way in which traditional conventions often interfered with formal reasoning that they advocated starting from scratch.

The design of Funmath adhered to the same stringent requirements, but revealed that the "look and feel" of familiar conventions could be salvaged by resynthesizing to a larger extent than originally anticipated. Eliminating defects separately in an ad hoc fashion is obviously out of the question. To do so, there are manipulation tasks for students at every grade level. For example, a 6th grade geometry activity involves using geoboards to illustrate area, perimeter and rational number concepts.

Ideal for classes with one-to-one device use, the website can also act as a learning station. Add a game-like spin to content reviews by playing Initials. Hand a unique sheet to each student that has problems aligned with a common skill or topic. The exercise continues until all questions on each sheet have answers, encouraging students to build trust and teamwork. Divide your class into two teams to play math baseball — an activity that gives you full control of the questions students answer.

If the at-bat team answers incorrectly, the defending team can correctly respond to earn an out. After three outs, switch sides. Play until one team hits 10 runs, or five for a shorter entry or exit ticket. Play Around the Block as a minds-on activity, using only a ball to practice almost any math skill.

First, compile questions related to a distinct skill. Second, have students stand in a circle. Finally, give one student the ball and read aloud a question from your list. Students must pass the ball clockwise around the circle, and the one who started with it must answer the question before receiving again. If the student incorrectly answers, pass the ball to a classmate for the next question. If the student correctly answers, he or she chooses the next contestant.

Pair students to compete against one another while building different math skills in this take on tic-tac-toe. To prepare, divide a sheet into squares — three vertical by three horizontal. Fill these squares with questions that collectively test a range of abilities. The first student to link three Xs or Os — by correctly answering questions — wins.

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This game can be a learning station , refreshing prerequisite skills in preparation for new content. Put a mathematical twist on a traditional card game by having students play this version of War. Students should pair together, with each pair grabbing two decks of cards. Cards have the following values:. Each student will always play two cards at a time, but younger kids must subtract the lower number from the higher. Older students can multiply the numbers, designating a certain suit as having negative integers.

Whoever has the highest hand wins all four cards. Cover core skills by visiting TeacherTube — an education-only version of YouTube. By searching for a specific topic or browsing by category, you can quickly find videos to supplement a lesson or act as a learning station.

Have a Blast Mastering Math Concepts

Students and parents can also visit TeacherTube on their own time, as some videos explicitly apply to them. Add the person on Skype or Google Hangouts, delivering the lesson through the program. Skype even has a list of guest speakers who will voluntarily speak about their topics of expertise. Although the exercise traditionally spans across subjects through guided research, you can focus on math by requiring students to:.

For younger students, you can divide the activity into distinct exercises and allow them to work in groups. Older students should tackle it as an in-class or take-home project.


Celebrate Pi Day on March 14 each year by dedicating an entire period, or more, to the mathematical constant. Although specific activities depend on your students, you can start the lesson by giving a historical and conceptual overview of pi — from Archimedes to how modern mathematicians use it. After, delve into exercises.

The problems range in difficulty and for many the experience is inductive chain learning. That is, by solving one problem it will expose you to a new concept that allows you to undertake a previously inaccessible problem. In order to track your progress it is necessary to setup an account and have Cookies enabled.