Michael Serra
http://www.michaelserra.net/weblog/
enUS
20140218T17:19:1208:00

Descubriendo la Geometría La Serie de Video
http://www.michaelserra.net/weblog/2014/02/descubriendolageometr%C3%ADalaseriedevideo.html
Introducing the new Discovering Geometry Spanish Video Series! Check out our sample investigation below and the trailer for the Discovering Geometry Spanish Video Subscription here. DG43.7.3 Incentro from Michael Serra on Vimeo. Subscribe to the rest of our Spanish tutorials...
<p>Introducing the new Discovering Geometry Spanish Video Series! Check out our sample investigation below and the trailer for the Discovering Geometry Spanish Video Subscription <a title="Spanish Video Series Trailer" href="https://vimeo.com/91435153" target="_self">here</a>.</p>
<p><iframe allowfullscreen="" frameborder="0" height="281" mozallowfullscreen="" src="//player.vimeo.com/video/90816063?portrait=0" webkitallowfullscreen="" width="500"></iframe></p>
<p><a href="http://vimeo.com/90816063">DG43.7.3 Incentro</a> from <a href="http://vimeo.com/user18103371">Michael Serra</a> on <a href="https://vimeo.com">Vimeo</a>.</p>
<p> </p>
<p>Subscribe to the rest of our Spanish tutorials on Vimeo OnDemand. Chapters 411 coming soon!</p>
<p><a class="assetimglink" style="display: inline;" title="Ch.3 Spanish" href="https://vimeo.com/ondemand/13042" target="_self"><img class="asset assetimage atxid6a0105365f9066970b01a51199dcaf970c imgresponsive" title="Ch.3 Spanish" src="http://www.michaelserra.net/.a/6a0105365f9066970b01a51199dcaf970c120wi" alt="IStock_000018638153_Medium" /></a></p>
<p><a title="Ch.3 Spanish" href="https://vimeo.com/ondemand/13042" target="_self">Ch.3 Using Tools of Geometry (Spanish)</a><br /> </p>
<p> </p>
Descubriendo la Geometría La Serie de Video
Michael Serra
20140218T17:19:1208:00

Welcome
http://www.michaelserra.net/weblog/2013/08/welcome.html
For over thirty years I’ve been able to do what I love: teach mathematics. Teaching has led me on a wonderful journey from working with high school students writing Discovering Geometry and other math materials, and sharing my professional development...
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<p> </p>
<p><span style="fontfamily: Arial; fontsize: 15px;"><span style="fontfamily: Arial; fontsize: 15px;"><span style="fontsize: 13px;"><span style="fontsize: 13px;">For over thirty years I’ve been able to do what I love: teach mathematics.  Teaching has led me on a wonderful journey from working with high school students</span></span></span></span><span style="fontsize: 13px;"><span style="fontsize: 14px;"><span style="fontsize: 13px;"> writing <a href="http://www.michaelserra.net/weblog/discoveringgeometrytext/" target="_blank">Discovering Geometry</a> and other math materials, and sharing my professional development services with fellow educators.</span></span></span></p>
<p><span style="fontsize: 17px;"><span style="fontsize: 14px;"><span style="fontsize: 13px;">Most recently my path has led me to some exciting classes as the “mathemagician” with local fifth grade students. </span></span></span><span style="fontfamily: Arial;"><span style="fontsize: 10pt;">These youngsters explored algebra, geometry, and probability, through a variety of games and puzzles and they did it with delight and enthusiasm. No math anxiety here!</span></span><span style="fontsize: 17px;"><span style="fontsize: 14px;"><span style="fontsize: 13px;"> <br /></span></span></span></p>
<p><span style="fontsize: 17px;"><span style="fontsize: 14px;"><span style="fontsize: 13px;">Please browse through our website and see all of the materials which are available:  DG textbook, math supplements, the Games and Puzzles series, geometry videos, and scheduled speaking engagements.</span></span></span> <span style="fontsize: 17px;"><span style="fontsize: 14px;"><span style="fontsize: 13px;">Please feel free to contact us for professional development for your school or district. If you were a past student or participant who enjoyed my classes, please let us know. We look forward to hearing from you.</span></span><span style="fontsize: 14px;"><span style="fontsize: 13px;"><br /></span></span></span></p>
<p><span style="fontsize: 17px;"><span style="fontsize: 14px;"><span style="fontsize: 13px;">Sincerely,</span></span> <span style="fontsize: 14px;"><span style="fontsize: 13px;">Michael</span></span></span></p>
<p class="MsoNormal" style="margin: 0in 0in 6pt;"><span style="fontfamily: Arial;"><span style="fontsize: small;"><span style="fontfamily: Arial; fontsize: 13px;"><a href="mailto:mserramath@gmail.com">mserramath@gmail.com</a></span></span></span></p>
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Michael Serra
20130805T13:12:0007:00

Proof in Discovering Geometry
http://www.michaelserra.net/weblog/2013/08/proofindiscoveringgeometry.html
Proof in Discovering Geometry pdf Geometry has traditionally been the course in which a deductive structure is first taught and formalized. This is tradition, but not good pedagogy. In a subject that is highly visual we ask students to deny...
<p><strong>
<span class="asset assetgeneric atxid6a0105365f9066970b0191049827ad970c">
<span class="asset assetgeneric atxid6a0105365f9066970b019104985699970c"><a href="http://www.michaelserra.net/files/proofindiscoveringgeometry.pdf">Proof in Discovering Geometry pdf</a></span></span><em> </em></strong></p>
<p>Geometry
has traditionally been the course in which a deductive structure is first
taught and formalized. This is tradition, but not good pedagogy. In a subject
that is highly visual we ask students to deny what they see until they have
performed this mysterious ritual called a twocolumn proof. </p>
<p><strong>The van Hiele Model </strong></p>
<p>Whenever
there is discussion about proof in geometry we should first review the research
of Dina van HieleGeldorf and her husband Pierre van Hiele. Their research
resulted in the van Hiele model of geometric reasoning. Research by numerous
mathematics educators including Usiskin 1982; Senk 1985; Burger and Shaughnessy
1986; Geddes and Fry 1988; Clements and Battista 1992; and more recently
Battista 2007, support the accuracy of the van Hiele model. The model consists
of five levels of geometric reasoning that students pass through from pre
deductive visual thinking to an understanding of formal proof and mathematical
structures.</p>
<p>Level 0:        <strong><em>Visualization</em></strong>
–students can identify rectangles by sight but squares are squares and are not
seen as special rectangles. </p>
<p>Level 1:         <strong><em>Analysis</em></strong>
(descriptive) – students can identify properties of rectangles (by drawing,
measuring, and making models) but cannot yet derive other properties from
given. </p>
<p>Level 2:        <strong><em>Informal
Deduction</em></strong> – students can give an informal argument to justify that the
figure is a rectangle from given properties.</p>
<p>Level 3:        <strong><em>Formal
Deduction</em></strong> – students are capable of creating original logical
arguments.</p>
<p>Level 4:        <strong><em>Rigor</em></strong>
– students are capable of reasoning about mathematical structures (i.e.
Euclidean vs. nonEuclidean geometries).</p>
<p>The
van Hiele model asserts these levels are sequential and hierarchical. That
is, students cannot move to the next higher level until they have successful
mastered the previous level. Furthermore movement from a lower level to the
next higher level depends more on content and pedagogy than on maturity and age.
</p>
<p>The
van Hiele research shows students aren’t ready for formal proof until they
have had concrete experiences with geometric figures and have successfully
mastered earlier levels of visual thinking. Research shows 70% of high
school students enter geometry operating at level 0 or 1 on the van Hiele
measure of geometric reasoning (Shaughnessy and Burger 1985; Senk 1989). Yet
"traditional" geometry textbooks that begin with establishing
postulates and proving theorems are expecting students to immediately begin
their geometry experience at levels 34. When the teacher and the textbook are
presenting geometry at van Hiele level 3 or higher, while the students are
functioning at level 0 or 1, it should be no surprise that there is such a high
failure rate in traditional geometry courses.</p>
<p>From
<em>Mathematician's Delight</em> by English
Mathematician W.W. Sawyer (19112008)</p>
<p><em>It would, I suppose, be quite possible to teach a deaf and dumb
child to play the piano. When it played a wrong note, it would see the frown of
its teacher, and try again. But it would obviously have no idea of what it was
doing, or why anyone should devote hours to such an extraordinary exercise. It
would have learnt an imitation of music. And it would fear the piano exactly as
most students fear what is suppose to be mathematics.</em></p>
<p>Some
geometry teachers claim they can successfully teach all of their geometry
students how to create geometry proofs. Perhaps they only have those 30% that
are entering geometry and functioning above van Hiele levels 0 and 1. I suspect
however, they may also be teaching an "imitation geometry." Their
students are trained to go through the motions of stating the theorem about to
be proved (5 points), then stating the given (5 points), then stating the show
(5 points), then drawing the diagram to the right (5 points), then drawing the
big T (5 points), then putting the given information in the first few lines of
the Tproof (515 points), then writing given to the right of each statement
(515 points), then throwing in enough statements to garner enough points to
get credit for the exercise without having any clue as to what he or she was
doing or why anyone should devote hours to such an extraordinary exercise. They
are doing imitation geometry.</p>
<p><em>Discovering Geometry</em>, in its first edition, was an innovator
in addressing students’ needs for gradual development of the deductive process.
<em>Discovering Geometry</em> is the only high
school geometry textbook on the market that is aligned with the van Hiele model
and other research on geometric proof. We accept the vast majority of
student are entering geometry at very low van Hiele levels of geometric
reasoning and our goal, with careful deliberate scaffolding, is to move them to
higher and higher levels of geometric reasoning as they progress through the
course. </p>
<p><strong>The Role and Function of Proof </strong></p>
<p>Geometry
student's consistent difficulties with understanding proofs (an international
problem BTW) should not be solely attributed to their inability to reason but
perhaps our inability to recognize there are many purposes for doing
proofs and we have been stressing the wrong purposes for proof at inappropriate
times. Professor Michael de Villiers' research on the role and function of
proof identifies six basic roles for proof: </p>
<p><strong>•    Verification
–</strong>to remove doubt, to
convince someone of the truth of a statement</p>
<p><strong>•    Systematization
</strong>–organize known results
into a deductive system of postulates, definitions, and theorems</p>
<p><strong>•    Explanation
</strong>–insight into why
something is true </p>
<p><strong>•    Discovery
</strong>–proof can occasionally
lead to new unexpected results </p>
<p><strong>•    Communication
</strong>–proof can create a
forum for critical debate</p>
<p><strong>•    Intellectual
Challenge </strong>–proof can be
a testing ground for intellectual stamina and ingenuity</p>
<p> </p>
<p>The
function of proof in a high school geometry course has been mostly twofold: to
remove doubt, to convince someone of the truth of a statement –<strong>verification</strong> and to establish geometry
as a mathematical system –<strong>systematization</strong>.
</p>
<p>Many
high school mathematics teachers seem to hold this naive view the main
function of proof is to provide verification that a given statement is true.
The role of proof as a means of verification is a useful method of verifying
the "truth" of a proposition within a mathematical system, especially
when coming across surprising (nonintuitive) results. However this view does
not stand up to actual mathematician's experiences. Professor George Polya
wrote, “When you have satisfied yourself that the theorem is true, you start
proving it.” If the sole or primary purpose for doing proofs in a high school
geometry course is to provide verification of the truth of a statement then
students functioning below level 4 on the van Hiele scale will continue to
question, or worse, disregard the process of proof. </p>
<p>If
systematization is emphasized as a primary function of proof right from the start
of a geometry course, the same poor results will persist. The van Hiele model
tells us systematization requires the highest van Hiele level of geometric
reasoning. Geometry textbooks that begin their geometry program with lists of
definitions and postulates, and then begin doing twocolumn proofs are ignoring
the research. Only an honors course or any class in which all students are
finally operating at van Hiele level 4 would have any chance of success in a
course that looks at geometry from the perspective of a mathematical system. Until
some magic happens and all students beginning geometry enter the course
functioning at van Hiele level 3, any attempt to create a mathematical system
for a regular or informal geometry course is likely to continue to have major
problems.</p>
<p>Students
can acquire a very high degree of confidence in a conjecture arrived at by
inductive methods but these methods may not explain why the conjecture is true.
Here is where proof can come to the rescue. An example would be the inductive
discovery that the sum of the measures of the three angles of a triangle is
always 180°. A good inductive first approach would be to ask students to
measure the three angles of a number of triangles thus gaining reasonable
confidence the sum is indeed 180°. The same can be done with dynamic
geometry software. Either investigative approach is a good first step because
it is the first approach students would take. These inquiry approaches do give
students confidence in their conjecture however they give no insight as to why
the sum is always 180°. The investigation should be followed by a second
investigation where they cut out the triangle and then tear off two of the
angles and arrange them on both sides of the third angle to create a straight
line. From this arrangement they can see the three angles create a line
parallel to the third side. This visually explains what properties this
conjecture is dependent upon and why the conjecture is true. This can also be
done quickly with a patty paper investigation. </p>
<p>From
<em>The Role and Function of Proof in
Mathematics</em> by Michael de Villiers:</p>
<p><em> It is not a question
of "making sure," but rather a question of "explaining
why."</em></p>
<p><strong>Explanation as the Primary Role of
Proof </strong></p>
<p>Using
proof as a means of explaining why something is true is the most meaningful
role proof can play in a high school geometry course. Asking why something is
true, after performing investigations that have convinced students it is
true, is a powerful 12 punch. Explaining why can be an effective tool
regardless of a student's van Hiele level. This is the approach we take with <em>Discovering Geometry</em>. </p>
<p>In
practically every lesson in the fourth edition of <em>Discovering Geometry</em> (DG4) students are asked to perform geometric
investigations and then make their geometry conjectures. After performing their
investigation and making their conjecture they are asked, "can you explain
why?" For example, after their very first two investigations leading to
geometric conjectures, the Linear Pair Conjecture and the Vertical Angles
Conjecture, students are asked:</p>
<p>"<strong><em>Developing
Proof </em></strong>You used inductive reasoning to discover both the Linear Pair
Conjecture and the Vertical Angles Conjecture. Are they related? If you accept
the Linear Pair Conjecture as true, can you use deductive reasoning to show
that the Vertical Angles Conjecture must be true?"</p>
<p>We
then ask them to work with their cooperative group members to develop a
paragraph proof explaining why the conjecture is true then check their
reasoning with ours. </p>
<p>Later
after discovering the Triangle Sum Conjecture students are asked:</p>
<p>"<strong><em>Developing
Proof </em></strong>The investigation may have convinced you that the Triangle Sum
Conjecture is true, but can you explain <em>why</em>
it is true for every triangle?"</p>
<p>We
then direct them to look back at the arrangement of the three angles they
tore off and reassembled forming a line. We ask, "how is the resulting
line related to the original triangle?" This is their leadin to creating a
paragraph proof explaining why their conjecture fits with what they have
already discovered/proved about parallel lines. </p>
<p>The
inductive and deductive reasoning in DG4 continues with investigating,
conjecturing, and explaining why, from Chapter 2 through Chapter 12. It isn't
until the last chapter, when there may be students ready for van Hiele level 4
reasoning, that we introduce geometry as a formal mathematical system. </p>
<p>Again
from <em>Mathematician's Delight</em> by
English Mathematician W.W. Sawyer (19112008)</p>
<p><em>The Great Pyramid was built in 3900 B.C. by rules based on
practical experience: Euclid's system did not appear until 3,600 </em>years later<em>. It is quite unfair to expect children to start studying
geometry in the form that Euclid gave it. One cannot leap 3,600 years of human
effort so lightly! The best way to learn geometry is to follow the road which
the human race originally followed: </em>Do<em> things, </em>make<em> things, </em>notice<em>
things, </em>arrange<em> things, and only then –</em>reason<em> about things. </em></p>
<p>Once
deductive arguments began to sprout up around Ancient Greece, it still took awhile for the process to be accepted. From the first deductive arguments by
Thales to Euclid's Elements, it took over 300 years. We owe it to our students to
give them time to move up through the van Hiele levels so they come to
understand the role proof plays in mathematics.</p>
<p><em> </em></p>
Michael Serra
20130805T13:09:1107:00

Discovering Geometry Supplements
http://www.michaelserra.net/weblog/2011/08/resourcesforteachingandlearningdiscoveringgeometryincludesalloftheteachingresourcesnecessarytoenrichlearning.html
Discovering Geometry includes all of the teaching resources necessary to enrich learning and to make the teaching experience more rewarding. In addition to a comprehensive, wraparoundstyle Teacher's Edition, you'll receive a spectrum of evaluation and assessment tools that let all...
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</div>
<p> </p>
<p> </p>
<p><em>Discovering Geometry</em> includes all of the teaching resources necessary to enrich learning and to make the teaching experience more rewarding. In addition to a comprehensive, wraparoundstyle <em>Teacher's Edition</em>, you'll receive a spectrum of evaluation and assessment tools that let all students demonstrate what they have learned. Broad input from teachers has made the teaching resources package a valuable asset for teachers implementing this exciting curriculum.You can purchase DG publications through our publisher <a href="http://www.kendallhunt.com/K12ProgramComponents.aspx?id=24592" target="_blank" title="Kendall Hunt">Kendall Hunt</a>.</p>
<p>The <em>Discovering Geometry® Video Series</em> is available in English and will be availble in 2014 in Spanish. Please go to <a href="http://www.michaelserra.net/weblog/discoveringgeometryvideosubscription.html" target="_blank" title="">DG Video subscriptions</a> for information.</p>
<div> </div>
<p> </p>
Discovering Geometry Supplements
Michael Serra
20110801T19:31:0007:00

Smart Moves Back Cover and Sample
http://www.michaelserra.net/weblog/2011/05/smartmovesbackcoverandexcerpt.html
Contents Chapter 1 Warm Up Puzzles 1.1 Color Network Puzzles 1.2 Square Route Puzzles 1.3 Container Puzzles 1.4 Sequential Movement Puzzles 1.5 Cryptarithm Puzzles 1.6 Robot Programming Puzzles Chapter 2 The Game of Racetrack 2.1 Racetrack 2.2 Mathematical Connections: Vectors...
<p>
<a class="assetimglink" href="http://www.michaelserra.net/.a/6a0105365f9066970b017eeaaff149970dpi" style="display: inline;"><img alt="SM Back cvr" border="0" class="asset assetimage atxid6a0105365f9066970b017eeaaff149970d imagefull" src="http://www.michaelserra.net/.a/6a0105365f9066970b017eeaaff149970d800wi" title="SM Back cvr" /></a><br /> <br /><br /></p>
<p><strong>Contents</strong><strong> </strong></p>
<p><strong>Chapter 1   Warm Up Puzzles </strong></p>
<p>1.1   Color Network Puzzles<strong> </strong></p>
<p>1.2   Square Route Puzzles<strong> </strong></p>
<p>1.3   Container Puzzles<strong> </strong></p>
<p>1.4   Sequential Movement Puzzles<strong> </strong></p>
<p>1.5   Cryptarithm Puzzles<strong> </strong></p>
<p>1.6   Robot Programming Puzzles<strong> </strong></p>
<p><strong>Chapter 2   The Game of Racetrack</strong></p>
<p>2.1   Racetrack</p>
<p>2.2   Mathematical Connections: Vectors</p>
<p><strong>Chapter 3   Movement Puzzles</strong></p>
<p>3.1   Coin Puzzles</p>
<p>3.2   Sliding Block Puzzles</p>
<p>3.3   Queen Bee Puzzles</p>
<p>3.4   Mini Robot Puzzles</p>
<p>3.5   Mathematical Connections: Archimedean Tilings</p>
<p><strong>Chapter 4  Tour Puzzles</strong></p>
<p>4.1   Rook’s Tour Puzzles</p>
<p>4.2   King’s Tour Puzzles</p>
<p>4.3   Knight’s Tour Puzzles</p>
<p>4.4   Mathematical Connections: Euler Paths</p>
<p><strong>Chapter 5  Magic Square Puzzles</strong></p>
<p>5.1   Introduction to Magic Squares</p>
<p>5.2   3x3 Magic Squares</p>
<p>5.3   4x4 Magic Squares</p>
<p>5.4   5x5 Magic Squares</p>
<p>5.5   6x6 and 7x7 Magic Squares</p>
<p>5.6   8x8 Magic Squares</p>
<p>5.7   12x12 Magic Squares</p>
<p><strong>Chapter 6   Sequential Reasoning and Algebra</strong></p>
<p>6.1   Algebraic Magic Square Puzzles</p>
<p>6.2   Squaring the Square Puzzles</p>
<p>6.3   Number Chase Puzzles</p>
<p><strong>Chapter 7   Sequential Reasoning and Geometry</strong></p>
<p>7.1   Angle Chase Puzzles</p>
<p><strong>Appendices            </strong></p>
<p>A.1   Racetracks</p>
<p>A.2   Playing Boards</p>
<p>A.3   Properties of Algebra</p>
<p>A.4   Properties of Geometry</p>
<p>A.5   Hints</p>
<p>A.6   Answers</p>
<p>A.7   Proofs</p>
<p><strong><br /></strong></p>
<p><strong>Sample Sequential Reasoning Puzzles</strong></p>
<p><strong> </strong><strong><br /></strong><em> </em></p>
<p><strong>Color Network Puzzle</strong><br />Each circle is to be colored Red (R), Yellow (Y), or Blue (B).  However no two vertices of a triangle are permitted to be the same color. What must be the color of the circle marked with a question mark? </p>
<p>                                      <a href="http://www.michaelserra.net/.a/6a0105365f9066970b01157225d61b970bpi" style="display: inline;"><img alt="Image003" border="0" src="http://www.michaelserra.net/.a/6a0105365f9066970b01157225d61b970b800wi" title="Image003" /></a></p>
<p> <strong>Tour Puzzles</strong></p>
<p>A knowledge of chess is not necessary in order to solve these puzzles. A rook moves horizontally or vertically, but not diagonally. Fill in the missing numbers 1 49 for puzzle 14. For puzzle 20, fill in the missing numbers to generate a continuous path in each square.</p>
<p><strong> </strong></p>
<p> </p>
<p><strong>Rook's Tour Puzzle 14 h    </strong>    <strong>Rook's Tour Puzzle 20</strong></p>
<p><strong> </strong>   <a href="http://www.michaelserra.net/.a/6a0105365f9066970b011572258df0970bpi" style="display: inline;"><img alt="Image017" border="0" src="http://www.michaelserra.net/.a/6a0105365f9066970b011572258df0970b800wi" title="Image017" /></a>          <a href="http://www.michaelserra.net/.a/6a0105365f9066970b01157131071e970cpi" style="display: inline;"><img alt="Image014" border="0" src="http://www.michaelserra.net/.a/6a0105365f9066970b01157131071e970c800wi" title="Image014" /></a></p>
<p> </p>
<p><strong>Mathematical Connections: Euler Paths</strong></p>
<p>If all the edges of a network, called a <strong>graph</strong> in Graph Theory, can be covered without retracing any edge, then the graph has an <strong>Euler path</strong>. If all edges of a graph can be covered without repetition and you can return to the starting point, then the graph has an <strong>Euler circuit</strong>.</p>
<p> </p>
<p><strong>Magic Squares</strong></p>
<p><strong> </strong>A Magic Square is a square array of distinct integers such that the numbers in any row, column, or main diagonals, have the same sum (called the magic sum). The magic square below is a normal 4x4 magic square.</p>
<p>                <a href="http://www.michaelserra.net/.a/6a0105365f9066970b011571310f5e970cpi" style="display: inline;"><img alt="Image023" border="0" src="http://www.michaelserra.net/.a/6a0105365f9066970b011571310f5e970c800wi" title="Image023" /></a></p>
<p><br /><strong> </strong>A magic square puzzle is an incomplete magic square.  Complete the 5x5 magic square.  You will need to calculate the magic sum first.</p>
<p>                        <strong>Magic Square Puzzle 36<br /></strong></p>
<p>                         <a href="http://www.michaelserra.net/.a/6a0105365f9066970b011572259755970bpi" style="display: inline;"><img alt="Image020" border="0" src="http://www.michaelserra.net/.a/6a0105365f9066970b011572259755970b800wi" title="Image020" /></a></p>
<p> </p>
<p><strong>Angle Chase Puzzles </strong></p>
<p><br />Students rely on their recall of geometry properties (and can review them in Appendix 4), not their protractor, when solving Angle Chase puzzles. The puzzle below uses properties of parallels, vertical angles, isosceles triangle properties, and polygon sum properties. Find the measures of all the angles in the Angle Chase puzzle below.</p>
<p><a href="http://www.michaelserra.net/.a/6a0105365f9066970b01157130ffe0970cpi" style="display: inline;"><img alt="Image005" border="0" src="http://www.michaelserra.net/.a/6a0105365f9066970b01157130ffe0970c800wi" title="Image005" /></a></p>
<p> </p>
<p><strong>Summary</strong></p>
<p><strong> </strong>This article describes four different sequential reasoning puzzles (and each puzzle has many variations). These puzzles, played as part of your school mathematics curriculum, make great classroom openers, end of period thought provokers, or for students to work on at home during school breaks. The puzzles in <em>Smart Moves</em> are wonderful for cooperative problem solving activities in the classroom. You can project a worksheet onto a screen as the class solves the puzzle together.  I encourage parents to participate in these games and puzzles with the entire family.  Sequential reasoning puzzles can provide a setting for children and grandparents to work on problem solving and mental exercises together. Try them.  I think you’ll see the “reason” for including them in your lesson plans.<br /><br /></p>
Michael Serra
20110508T21:11:0007:00

ERRATA – SMART MOVES January 11, 2012
http://www.michaelserra.net/weblog/2011/05/erratasmartmovesjanuary112012.html
P. 8.  Robot Puzzle 1 instruction, change the last sentence “Write a program with 12 or fewer steps” to “Write a program with 14 or fewer steps.” P. 176.  RP Puzzle 1 answer should be: F8 TR TR...
<p><br /><br /><span style="fontsize: 12pt;"><strong>P. 8.   Robot Puzzle 1 instruction,</strong> change the last sentence</span><br /><span style="fontsize: 12pt;"> “Write a program with 12 or fewer steps” to “Write a program with 14 or fewer steps.”  </span><br /><br /><strong><span style="fontsize: 12pt;">P. 176.  RP Puzzle 1 answer should be:</span></strong><br /><span style="fontsize: 12pt;"> F8 TR TR F2 TR F4 TL F4 TR TR F5 TL F3 TL</span><br /><br /><strong><span style="fontsize: 12pt;">P. 179. – MR Puzzle 3 answer should be: </span></strong><br /><span style="fontsize: 12pt;">1 → 4 ↓ →</span></p>
<p> </p>
<p>Copyright © Michael Serra 2011</p>
Smart Moves
Michael Serra
20110508T21:10:0007:00

Developing Mathematical Reasoning with Games and Puzzles Series
http://www.michaelserra.net/weblog/2011/04/resourcepuzzlebookseries.html
Thank you to everyone who contacted us about our Developing Mathematical Reasoning with Games and Puzzles series. We are very excited to introduce the first book, Smart Moves. It was developed from my elementary, high school, and university classroom experiences....
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<p style="fontsize: 18px; fontfamily: Arial;"><strong><a href="http://www.michaelserra.net/.a/6a0105365f9066970b012876db9a56970cpi" style="display: inline;"><img alt="IMG_4889" border="0" class="asset assetimage atxid6a0105365f9066970b012876db9a56970c" src="http://www.michaelserra.net/.a/6a0105365f9066970b012876db9a56970c800wi" title="IMG_4889" /></a> <br /></strong></p>
<p style="fontsize: 15px; fontfamily: Arial;"><span style="fontsize: 15px; fontfamily: Arial;">Thank you to everyone who contacted us about our <em>Developing Mathematical Reasoning with Games and Puzzles</em> series. We are very excited to introduce the first book, <em>Smart Moves</em>.  It was developed from my elementary, high school, and university classroom experiences</span><span style="fontsize: 15px; fontfamily: Arial;">. <em>Smart Moves</em> will interest people of all ages from middle and high school students to seniors interested in keeping "brain fit". I sincerely hope you enjoy the experience!</span></p>
<p style="fontsize: 15px; fontfamily: Arial;"><span style="fontsize: 15px; fontfamily: Arial;"><br /></span></p>
<p style="fontsize: 15px; fontfamily: Arial;"><strong> </strong>   <a href="http://www.michaelserra.net/.a/6a0105365f9066970b014e61084529970cpi" style="display: inline;"><img alt="SM.Front coverFinal" class="asset assetimage atxid6a0105365f9066970b014e61084529970c" src="http://www.michaelserra.net/.a/6a0105365f9066970b014e61084529970c320wi" title="SM.Front coverFinal" /></a> <br /> <br /><br />•   <a href="http://www.michaelserra.net/weblog/2011/05/sequentialreasoningwoutline.html" target="_self"> </a><a href="http://www.michaelserra.net/weblog/2011/05/sequentialreasoningwoutline.html" target="_self">SMART MOVES  Sequential Reasoning</a></p>
<p style="fontsize: 15px; fontfamily: Arial;"><br /><strong>Target Audience:</strong><br />•    5 12 public and private school teachers<br />•    High school and middle school math teachers<br />•    Intergenerational activities for grandparents, parents, and children<br />•    Home schools, gifted students<br />•    Puzzle enthusiasts  <br />•    Post 50 babyboomers seeking brain exercises</p>
<p style="fontsize: 18px; fontfamily: Arial;"><strong>Why our game/puzzle books are unique <br /></strong></p>
<p style="fontsize: 15px; fontfamily: Arial;">Most puzzle books are simply a collection of games and puzzles.  Our series shows the connection between certain games and puzzles and mathematical thinking. Mathematical thinking requires reasoning skills which are useful in everyday life. Studies have shown that people learn better when they are relaxed and enjoying themselves.  Experienced teachers are aware of this fact and incorporate gamebased learning into their lesson plan to increase motivation and promote retention. The series presents a unique opportunity for participants to have fun while developing important sequential reasoning skills.</p>
<p style="fontsize: 15px; fontfamily: Arial;">Below is a puzzle from a future book in the series.</p>
<p><a href="http://www.michaelserra.net/files/test.pdf"></a><a href="http://www.michaelserra.net/files/bagelspuzzle1answer.only.2forwebsite.pdf"></a><a href="http://www.michaelserra.net/files/bagelspuzzle.pdf">Download Bagels Puzzle (PDF)<br /></a></p>
<p><a href="http://www.michaelserra.net/files/test.pdf"></a><a href="http://www.michaelserra.net/files/bagelspuzzleanswer.pdf">Download Bagels Puzzle Answer (PDF)</a></p>
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Developing Mathematical Reasoning with Games and Puzzles
Michael Serra
20110418T12:58:0807:00

Thank you for your payment
http://www.michaelserra.net/weblog/2011/04/thankyouforyourpayment.html
Thank you for your payment. Your transaction has been completed, and a receipt for your purchase has been emailed to you. You may log into your account at www.paypal.com/us to view details of this transaction.
<p>Thank you for your payment. Your transaction has been completed, and a receipt for your purchase has been emailed to you. You may log into your account at <a href="https://www.paypal.com/us/">www.paypal.com/us</a> to view details of this transaction.</p>
Michael Serra
20110415T18:37:0007:00

Workshop Description
http://www.michaelserra.net/weblog/2011/01/workshopdescription.html
Workshops are generally one to three hours long and focus on a single topic. School districts will often contract Michael for a series of workshops once a week or twice monthly over a four to eight week period. Some examples...
<p><span style="fontsize: small;">Workshops are generally one to three hours long and focus on a single topic.<span>  </span>School districts will often contract Michael for a series of workshops once a week or twice monthly over a four to eight week period.<span>  </span>Some examples can be seen below. </span></p>
<p><span style="fontfamily: Trebuchet MS; fontsize: 15px;"><span style="fontsize: small;"><a href="http://www.michaelserra.net/weblog/formatpricing/">Pricing</a> is based on length of time,<strong> </strong>the number of visits, topics requiring special equipment and materials, and amount of travel involved.<span> For more information please contact us at <a href="mailto:%20mserramath@gmail.com">mserramath@gmail.com</a>.<br /></span></span></span></p>
Workshop Description
Michael Serra
20110101T23:11:0008:00

Lecture Videos
http://www.michaelserra.net/weblog/2010/12/investigationsingeometryfor2010saturdaynovember620108301000amsession561ignitehowtoteachmathanxie.html
How to Teach Math Anxiety What is Ignite? Ignite is a way to impart thoughtprovoking ideas in a fun and social way. I think Ignite is like "speed dating" because they feature nine speakers for five minutes with visuals changing...
<p><strong><span style="fontsize: 11pt;">How to Teach Math Anxiety</span></strong> </p>
<p>What is Ignite? Ignite is a way to impart thoughtprovoking ideas in a fun and social way. I think Ignite is  like "speed dating" because they feature nine speakers for five minutes with visuals changing every 15 seconds. I was honored to be invited to speak and here we go...</p>
<p><iframe allowfullscreen="" frameborder="0" height="315" src="//www.youtube.com/embed/G57qemxBVoM" width="420"></iframe></p>
Michael Serra
20101231T10:32:0008:00