European Mathematical Society - Stephen Krulik
https://euro-math-soc.eu/author/stephen-krulik
enStrategy Games to Enhance Problem-Solving Ability in Mathematics
https://euro-math-soc.eu/review/strategy-games-enhance-problem-solving-ability-mathematics
<div class="field field-name-field-review-review field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><div class="tex2jax"><p>
In the introduction the authors explain the goal of their book. When two opponents are playing a board game they need some strategy to win or at least maximize the chances not to loose the game. Mastering such strategies is a skill that can also be used in solving a (mathematical) problem. They even give a table drawing parallels between playing (and winning) the game versus the steps in solving a problem. I believe this is only superficial and much better and deeper analogies do exist. Winning a game is just another problem, where you have to first understand the goal, learn the rules, and develop some strategy. By repeated playing, one learns which strategies work and most of all which strategies work consistently and are not just a lucky hap. The meta question is then whether this strategy can be generalized, to other problems of larger dimension or when the rules are inverted or only slightly changed etc. This is a general approach to solve any problem, whether the problem is mathematical or not.</p>
<p>
Once this has been made clear, the following chapters are basically an enumeration of games, stating the rules and the goal of the game. There is also what the authors call a "sample simulation" in which some moves or situations are simulated, pointing to some problems or possibilities, making suggestions, and sometimes asking questions to think about.</p>
<p>
The different chapters group games that are similar or just form variations of the same game or at least they have similar goals and thus may require similar strategies. We have a chapter on tic-tac-toe-like games, one chapter is called "blocking games" which can come in many different forms (nim is and example), another chapter deals with games where the strategy has to be continuously updated while playing and finally a "miscellaneous" chapter where, among others, several classic western games are found like checkers, dominoes, battleship,...</p>
<p>
So far, only the problems were formulated and the reader, or rather the players, are supposed to go through the steps that I sketched in the first paragraph: finding and analysing a winning strategy. The last chapter provides answers and hints to the problems in the previous chapters. What are possible strategies? For example what is the best first move to open the game? Sometimes a mathematical proof may exist for the claim that the one who starts (and makes no mistakes) will always win. However there are no mathematics involved here, although there could have been. And these mathematics need not always be connected with game theory.</p>
<p>
In an appendix, illustrations of the (empty) game boards are given, although their geometry should be clear already from the previous chapters. Even if these pages are cut from the book, they may be too small to play on. I do not see the advantage of adding these pages to the printed book. Perhaps an electronic version could be printed with some magnification factor.</p>
<p>
In conclusion, this is a nice collection of board games, and when pupils will play such games, they will develop some winning strategies for these games, and these skills will probably help in cultivating certain attitudes and perhaps working schemes to tackle mathematical problems. However it was certainly not the intention of the authors to involve mathematics in this book. I think however that it would not be very difficult to hook up several mathematical problems to these games, somewhat like what Matthew Lane did for video games in his book <a href="/review/power-unlocking-hidden-mathematics-video-games" target="_blank">Power Up</a>. But that would be a completely different book because here the focus is just the games and learning how to win them mostly by playing them, thereby avoiding all the mathematics and abstract game theory.</p>
</div></div></div></div><div class="field field-name-field-review-reviewer field-type-text field-label-inline clearfix"><div class="field-label">Reviewer: </div><div class="field-items"><div class="field-item even">Adhemar Bultheel</div></div></div><div class="field field-name-field-review-desc field-type-text-long field-label-hidden"><div class="field-items"><div class="field-item even"><div class="tex2jax"><p>
The author's leitmotif in this book is that when two players are trying to win a board game, they will develop a winning strategy which is very similar to the strategies and skills needed to solve other, more mathematical, problems. So they describe many of these board games with their rules and urge the reader to play these games several times until they see some strategy emerge. In a final chapter they give some hints about what such strategies may look like for each of these games. There are however no mathematics involved as such.</p>
</div></div></div></div><span class="vocabulary field field-name-field-review-author field-type-taxonomy-term-reference field-label-inline clearfix"><h2 class="field-label">Author: </h2><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/author/alfred-s-posamentier" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">alfred s. posamentier</a></li><li class="vocabulary-links field-item odd"><a href="/author/stephen-krulik" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">Stephen Krulik</a></li></ul></span><span class="vocabulary field field-name-field-review-publisher field-type-taxonomy-term-reference field-label-inline clearfix"><h2 class="field-label">Publisher: </h2><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/publisher/world-scientfic" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">World Scientfic</a></li></ul></span><div class="field field-name-field-review-pub field-type-number-integer field-label-inline clearfix"><div class="field-label">Published: </div><div class="field-items"><div class="field-item even">2017</div></div></div><div class="field field-name-field-review-isbn field-type-text field-label-inline clearfix"><div class="field-label">ISBN: </div><div class="field-items"><div class="field-item even">978-981-3146-341 (pbk)</div></div></div><div class="field field-name-field-review-price field-type-text field-label-inline clearfix"><div class="field-label">Price: </div><div class="field-items"><div class="field-item even">GBP 20.00</div></div></div><div class="field field-name-field-review-pages field-type-number-integer field-label-inline clearfix"><div class="field-label">Pages: </div><div class="field-items"><div class="field-item even">136</div></div></div><span class="vocabulary field field-name-field-review-class field-type-taxonomy-term-reference field-label-hidden"><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/imu/mathematics-education-and-popularization-mathematics" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">Mathematics Education and Popularization of Mathematics</a></li></ul></span><div class="field field-name-field-review-website field-type-text field-label-hidden"><div class="field-items"><div class="field-item even"><a href="http://www.worldscientific.com/worldscibooks/10.1142/10187" title="Link to web page">http://www.worldscientific.com/worldscibooks/10.1142/10187</a></div></div></div><span class="vocabulary field field-name-field-review-msc field-type-taxonomy-term-reference field-label-hidden"><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/msc/97-mathematics-education" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">97 Mathematics education</a></li></ul></span><span class="vocabulary field field-name-field-review-msc-full field-type-taxonomy-term-reference field-label-hidden"><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/msc-full/97a20" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">97A20</a></li></ul></span><span class="vocabulary field field-name-field-review-msc-other field-type-taxonomy-term-reference field-label-hidden"><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/msc-full/00a08" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">00a08</a></li><li class="vocabulary-links field-item odd"><a href="/msc-full/91a05" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">91A05</a></li></ul></span>Fri, 23 Jun 2017 11:37:34 +0000Adhemar Bultheel47737 at https://euro-math-soc.euhttps://euro-math-soc.eu/review/strategy-games-enhance-problem-solving-ability-mathematics#commentsProblem-Solving Strategies in Mathematics From Common Approaches to Exemplary Strategies
https://euro-math-soc.eu/review/problem-solving-strategies-mathematics-common-approaches-exemplary-strategies-0
<div class="field field-name-field-review-reviewer field-type-text field-label-inline clearfix"><div class="field-label">Reviewer: </div><div class="field-items"><div class="field-item even"> </div></div></div><div class="field field-name-field-review-appendix field-type-file field-label-hidden"><div class="field-items"><div class="field-item even"><span class="file"><img class="file-icon" alt="PDF icon" title="application/pdf" src="/modules/file/icons/application-pdf.png" /> <a href="https://euro-math-soc.eu/sites/default/files/book-review/2017_ProblemSolvingStrategies_0.pdf" type="application/pdf; length=25740">2017_ProblemSolvingStrategies.pdf</a></span></div></div></div><span class="vocabulary field field-name-field-review-author field-type-taxonomy-term-reference field-label-inline clearfix"><h2 class="field-label">Author: </h2><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/author/alfred-s-posamentier-0" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">Alfred S Posamentier</a></li><li class="vocabulary-links field-item odd"><a href="/author/stephen-krulik" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">Stephen Krulik</a></li></ul></span><span class="vocabulary field field-name-field-review-publisher field-type-taxonomy-term-reference field-label-inline clearfix"><h2 class="field-label">Publisher: </h2><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/publisher/world-scientific-publishing-co-pte-ltd" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">World Scientific Publishing Co. Pte. Ltd.</a></li></ul></span><div class="field field-name-field-review-pub field-type-number-integer field-label-inline clearfix"><div class="field-label">Published: </div><div class="field-items"><div class="field-item even">2015</div></div></div><div class="field field-name-field-review-isbn field-type-text field-label-inline clearfix"><div class="field-label">ISBN: </div><div class="field-items"><div class="field-item even">978-981-4651-63-9 </div></div></div><div class="field field-name-field-review-pages field-type-number-integer field-label-inline clearfix"><div class="field-label">Pages: </div><div class="field-items"><div class="field-item even">188</div></div></div><span class="vocabulary field field-name-field-review-class field-type-taxonomy-term-reference field-label-hidden"><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/imu/mathematics-education-and-popularization-mathematics" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">Mathematics Education and Popularization of Mathematics</a></li></ul></span><span class="vocabulary field field-name-field-review-msc field-type-taxonomy-term-reference field-label-hidden"><ul class="vocabulary-list"><li class="vocabulary-links field-item even"><a href="/msc/97-mathematics-education" typeof="skos:Concept" property="rdfs:label skos:prefLabel" datatype="">97 Mathematics education</a></li></ul></span>Wed, 07 Jun 2017 16:48:59 +0000Eugenia47703 at https://euro-math-soc.euhttps://euro-math-soc.eu/review/problem-solving-strategies-mathematics-common-approaches-exemplary-strategies-0#comments