Here are links to a collection of free downloads of excellent books and resources for math teachers and others who enjoy math:
100 Great Problems of Elementary Mathematics (Dover) - Heinrich Dörrie.pdf - Google Drive
http://math.fau.edu/Yiu/RecreationalMathematics2003.pdf
Teaching Problem-solving in Undergraduate Mathematics
https://www.scientificamerican.com/media/pdf/Aug2008_Martin_Gardner_Recreational_Mathematics.pdf
https://kheavan.files.wordpress.com/2010/06/paul-zeitz-author-the-art-and-craft-of-problem-solving-2edwiley20060471789011.pdf
Schoenfeld: Learning to think mathematically: Problem solving, metacognition, and sense-making in mathematics.
Symmetries of the Plane
Creative Thinking in Mathematics with Tangrams and The Geometer’s Sketchpad
Larson's "Problem Solving through Problems"
Math Magic Archive
http://www.seacrest.org/uploaded/2009-2010/summer_math_packets/Entering_7th_grade_Math_Packet.pdf
Recreations in the Theory of Numbers
536 PUZZLES & CURIOUS PROBLEMS
Math from Three to Seven The Story of a Mathematical Circle for Preschoolers
http://www.wou.edu/~kruczekk/Courses/Math_396_Sp11/Coursepack396.pdf
Can you solve Martin Gardner’s best mathematical puzzles? | Science | The Guardian
https://rainymathboy.files.wordpress.com/2011/01/104-number-theory-problems.pdf
Aha! Solutions - Martin Erickson.pdf - Google Drive
Saturday, December 24, 2016
Saturday, December 17, 2016
PSM Workshop for Teachers -- Writing Math Quarter Exams
PREPARING MATH QUARTER EXAMS
Describe your typical process for writing each math quarter
exam.
Sample answers:
Find and copy last year’s exam
Use the unit tests from the publisher for the units covered
Complete the following: A good quarter exam in math …
~tests what was taught
~does not test what was not taught
~emphasizes important topics (e.g., if 3 weeks of instruction were devoted to a particular topic, then about 1/3 of the points on the test should be assigned to that topic)
~assesses every CCSS identified in the quarter outline
~assesses not just recall of facts, definitions, and memorized procedures but also higher order thinking
~challenges the strongest students in the class
~uses a variety of item types: multiple choice, short answer, extended response
~puts students under at least a slight pressure for time
~does not use any items identical to those the students have seen before
What materials should be at hand?
~textbook and relevant ancillary materials
~grade level pages from the CCSS
~quarter outline
~outside assessment resources
NEVER: anything from teacherspayteachers.com
RESOURCES
Find resources where items are keyed to CCSS.
https://www.illustrativemathematics.org/content-standards
Has links to CCSS tasks by grade level, starting with grade K.
North Carolina:
http://www.dpi.state.nc.us/indexRedirect.php?reqURL=accountability/testing/releasedforms (end-of-grade released forms; math and
ELA/Reading, grades 3-8)
New York:
Grades K-2 materials must be pulled out of the individual
modules:
find
the standards here: https://www.engageny.org/file/8771/download/ccls_checklist_for_a_story_of_units.pdf
https://www.engageny.org/resource/new-york-state-common-core-sample-questions grades 3-8, math and
ELA
Delaware:
PARCC (for grades 3-8)
https://parcc.pearson.com/practice-tests/math/
(answer key link provides CCSS for each sample item)
Achieve the Core (for grades 2-8)
http://achievethecore.org/category/1020/mathematics-assessments?&sort=name
Additional notes for PSM teachers: Check the Google Drive using the path PSMMathMarshaDVD--Workshops:Presentations--PSM 2016 teacher workshop preparing quarter exams to find materials related to this workshop and additional resources such as math clip art and images. Also on PSMMathMarshaDVD are grade-specific files containing a folder of assessment resources (mostly not keyed to the CCSS but possibly useful).
Additional notes for PSM teachers: Check the Google Drive using the path PSMMathMarshaDVD--Workshops:Presentations--PSM 2016 teacher workshop preparing quarter exams to find materials related to this workshop and additional resources such as math clip art and images. Also on PSMMathMarshaDVD are grade-specific files containing a folder of assessment resources (mostly not keyed to the CCSS but possibly useful).
Collect items!
Then check the match between items on the test and the
CCSS—in both directions.
Then arrange the items in a sensible order and assign points
to the items.
Do the points for each larger topic correspond to the amount
of instructional time devoted to the topic? Make adjustments to the points or
add items if needed.
Check for the variety of item types: multiple choice, short
answer, extended response.
Check for cognitive levels—are there enough basic level
items so that a student who has been paying attention in class, taking notes,
doing homework, and studying for exams can earn at least a grade of C? Do the
other items have the potential to spread the grades in a way that shows what
they know? Are there one or two items that will really challenge your best
students?
Is the test long enough to keep everyone profitably busy for
the entire time devoted to the exam?
After all this fine tuning, check on the layout of the
problems across pages—don’t strand the directions for a problem at the bottom
of one page with the item on the next page.
Take the test yourself to make sure the directions are clear
and you can create an unambiguous answer key.
Finally, highlight your master copy of the CCSS for your
grade level so you can see exactly which standards remain to be taught and
assessed during the rest of the school year. If you are preparing your third
quarter exam, make sure that what remains is doable. If not, it is better to
adjust NOW and change your third quarter instructional pace instead of rushing
to teach everything before your students take their standardized tests in the
spring.
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