<story><title>Many elementary teachers don’t understand math, and it makes them anxious</title><url>https://www.latimes.com/opinion/story/2019-11-21/math-anxiety-elementary-teacher</url></story><parent_chain><item><author>nopinsight</author><text>For those curious, below are some &lt;i&gt;kinds&lt;/i&gt; of primary math questions we model after to test teacher applicants.&lt;p&gt;In my experience, many kids are much more enthusiastic about this kind of &amp;quot;challenging&amp;quot; problems than the drills in many standard textbooks, as long as the problems are chosen to match their level. They definitely learn a lot more as well.&lt;p&gt;Note that although they do require a little arithmetic to solve, the challenging part is &lt;i&gt;not&lt;/i&gt; arithmetic.&lt;p&gt;Some problems focus on geometry, logic, patterns, or other kinds of puzzles. More examples can be found at the source below.&lt;p&gt;&amp;quot;- The edge of a cube is 8 cm. All the faces are painted orange. It is then cut into small cubes of edge 1 cm.
How many small cubes have exactly two faces painted?&lt;p&gt;- What is the greatest possible number one can get by discarding 100 digits, in any order, from the number 1234567891011121314151617…57585960?&lt;p&gt;- Eleven consecutive positive integers are written on a board. Maria erases one of the numbers. If the sum of the remaining numbers is 2012, what number did Maria erase?&lt;p&gt;- You must color each square in the figure below in red, green or blue. Any two squares with adjacent sides must be of a different color. In how many different ways can this coloring be done? 
Figure at question 11 here: &lt;a href=&quot;https:&amp;#x2F;&amp;#x2F;gato-docs.its.txstate.edu&amp;#x2F;jcr:450cce10-3b6a-4ddd-a195-5c26efe39bed&amp;#x2F;2012_PWMC_individual.pdf&quot; rel=&quot;nofollow&quot;&gt;https:&amp;#x2F;&amp;#x2F;gato-docs.its.txstate.edu&amp;#x2F;jcr:450cce10-3b6a-4ddd-a19...&lt;/a&gt; &amp;quot;&lt;p&gt;Source:
the Primary Math World Contest (usually held in Hong Kong)
&lt;a href=&quot;https:&amp;#x2F;&amp;#x2F;www.txstate.edu&amp;#x2F;mathworks&amp;#x2F;PMWC&amp;#x2F;previous-pmwc-tests.html&quot; rel=&quot;nofollow&quot;&gt;https:&amp;#x2F;&amp;#x2F;www.txstate.edu&amp;#x2F;mathworks&amp;#x2F;PMWC&amp;#x2F;previous-pmwc-tests.h...&lt;/a&gt;</text></item><item><author>nopinsight</author><text>For over a decade, I have run a successful tutoring center focused on math and science for elementary school students in a developing country. Our students won numerous awards both at the national and international levels.&lt;p&gt;We usually employ teachers with degrees in math or science, or sometimes engineering. Occasionally for early elementary levels (grades 1-3), some teachers have a degree in another discipline. Regardless of major, we &lt;i&gt;always&lt;/i&gt; test them for math aptitude. The test includes competitive exam questions focused on mathematical understanding and problem solving skills, rather than advanced math knowledge. (The other part of teacher selection is interviewing for teaching skills and trial teaching with student and expert evaluation.)&lt;p&gt;Somewhat surprisingly, even some PhD candidates in engineering may fail these tests, while a few liberal arts degree grads passed the lower levels of these tests. So math aptitude is not limited to those who majored in math, science, or engineering. (Note that many of our elementary school students who have studied with us for a couple of years also pass them at a high level.)&lt;p&gt;It seems that countries with successful math programs, like Singapore, also utilize a rigorous teacher selection process that favors subject matter specialists even for teaching at an elementary level.&lt;p&gt;This is crucial for math, which is particularly hard to catch up later on with shaky foundation.&lt;p&gt;(In fact, kids are great at absorbing their teacher’s attitude toward the subject. It is no surprise many kids may sense “math fear” from their teacher. Having a teacher with positive attitude toward the subject they teach is essential!)</text></item></parent_chain><comment><author>tacomonstrous</author><text>I&amp;#x27;m a working mathematician and would need a non-trivial amount of thought to get any of these problems.&lt;p&gt;I was also pretty poor at this kind of thing in high school and college, but fortunately the skills involved are almost but not quite disjoint from what is needed to do research on math.</text></comment>
<story><title>Many elementary teachers don’t understand math, and it makes them anxious</title><url>https://www.latimes.com/opinion/story/2019-11-21/math-anxiety-elementary-teacher</url></story><parent_chain><item><author>nopinsight</author><text>For those curious, below are some &lt;i&gt;kinds&lt;/i&gt; of primary math questions we model after to test teacher applicants.&lt;p&gt;In my experience, many kids are much more enthusiastic about this kind of &amp;quot;challenging&amp;quot; problems than the drills in many standard textbooks, as long as the problems are chosen to match their level. They definitely learn a lot more as well.&lt;p&gt;Note that although they do require a little arithmetic to solve, the challenging part is &lt;i&gt;not&lt;/i&gt; arithmetic.&lt;p&gt;Some problems focus on geometry, logic, patterns, or other kinds of puzzles. More examples can be found at the source below.&lt;p&gt;&amp;quot;- The edge of a cube is 8 cm. All the faces are painted orange. It is then cut into small cubes of edge 1 cm.
How many small cubes have exactly two faces painted?&lt;p&gt;- What is the greatest possible number one can get by discarding 100 digits, in any order, from the number 1234567891011121314151617…57585960?&lt;p&gt;- Eleven consecutive positive integers are written on a board. Maria erases one of the numbers. If the sum of the remaining numbers is 2012, what number did Maria erase?&lt;p&gt;- You must color each square in the figure below in red, green or blue. Any two squares with adjacent sides must be of a different color. In how many different ways can this coloring be done? 
Figure at question 11 here: &lt;a href=&quot;https:&amp;#x2F;&amp;#x2F;gato-docs.its.txstate.edu&amp;#x2F;jcr:450cce10-3b6a-4ddd-a195-5c26efe39bed&amp;#x2F;2012_PWMC_individual.pdf&quot; rel=&quot;nofollow&quot;&gt;https:&amp;#x2F;&amp;#x2F;gato-docs.its.txstate.edu&amp;#x2F;jcr:450cce10-3b6a-4ddd-a19...&lt;/a&gt; &amp;quot;&lt;p&gt;Source:
the Primary Math World Contest (usually held in Hong Kong)
&lt;a href=&quot;https:&amp;#x2F;&amp;#x2F;www.txstate.edu&amp;#x2F;mathworks&amp;#x2F;PMWC&amp;#x2F;previous-pmwc-tests.html&quot; rel=&quot;nofollow&quot;&gt;https:&amp;#x2F;&amp;#x2F;www.txstate.edu&amp;#x2F;mathworks&amp;#x2F;PMWC&amp;#x2F;previous-pmwc-tests.h...&lt;/a&gt;</text></item><item><author>nopinsight</author><text>For over a decade, I have run a successful tutoring center focused on math and science for elementary school students in a developing country. Our students won numerous awards both at the national and international levels.&lt;p&gt;We usually employ teachers with degrees in math or science, or sometimes engineering. Occasionally for early elementary levels (grades 1-3), some teachers have a degree in another discipline. Regardless of major, we &lt;i&gt;always&lt;/i&gt; test them for math aptitude. The test includes competitive exam questions focused on mathematical understanding and problem solving skills, rather than advanced math knowledge. (The other part of teacher selection is interviewing for teaching skills and trial teaching with student and expert evaluation.)&lt;p&gt;Somewhat surprisingly, even some PhD candidates in engineering may fail these tests, while a few liberal arts degree grads passed the lower levels of these tests. So math aptitude is not limited to those who majored in math, science, or engineering. (Note that many of our elementary school students who have studied with us for a couple of years also pass them at a high level.)&lt;p&gt;It seems that countries with successful math programs, like Singapore, also utilize a rigorous teacher selection process that favors subject matter specialists even for teaching at an elementary level.&lt;p&gt;This is crucial for math, which is particularly hard to catch up later on with shaky foundation.&lt;p&gt;(In fact, kids are great at absorbing their teacher’s attitude toward the subject. It is no surprise many kids may sense “math fear” from their teacher. Having a teacher with positive attitude toward the subject they teach is essential!)</text></item></parent_chain><comment><author>Shivetya</author><text>and here I sit totally flummoxed by the questions yet later on you state these were suitable to grades up to sixth?&lt;p&gt;So for those who have let their math skills lapse or need help to get back in the right frame of mind to learn, where online is the best resource?  Khan Academy?</text></comment>