New Mathematics Standards and Testing –
There is a lot of confusion about the new Common Core state standards adopted by most states in the nation and its accompanying testing. The latter half of the following article (scroll down about 14 paragraphs) has quite a bit of good information for parents about how the testing will change:
The key points are that these new standards and the testing being developed will have a diminished emphasis on students demonstrating that they know rules and procedures. Students will have complex, real life word problems to solve, and they will also have to explain how they arrived at their answer.
This is not to say that students will not need to learn the rules and procedures, but they will learn the rules by using manipulatives and pictures to solve cognitively complex mathematical problems and derive the rules in groups. Then, there will be a class discussion that will take place in which the teacher leads a discussion about the rule or procedure the students have derived so that students understand conceptually the most efficient procedure (these are the common rules and procedures from standard mathematics that everyone learns). Only then will students begin to use the newly-derived rule to solve more mathematical problems with the efficient algorithm they have derived and work to build their speed and fluency with the new procedure. This is the same way in which students in Singapore learn mathematics. Students in Singapore consistently prove on international mathematics testing that they are the best mathematics students in the world. They consistently are far more advanced in their skills than students in the United States, who fair poorly on conceptual and real world applications of mathematics (Van de Walle, Karp, and Bay-Williams, 2013).
The implications for parents are a few:
1) Your child may begin to struggle with the new mathematics instruction for a while.
2) From my discussions on forums for teachers of mathematics, it is clear that some teachers are adamantly resisting the change. The problem is that their students will not do well with the new testing. Basically, students will now need to not only learn the rules and procedures of mathematics, as we all did as children, but they will be expected to understand mathematics on a deeper, more conceptual level that will help them solve 21st Century problems (BTW… Good Common Core teaching practices do not throw out knowledge, speed, and fluency practice of the rules and procedures. That is a fallacy). It may be wise to have a discussion with your child’s mathematics teacher in order to find out how they are adapting to teach the new standards.
3) Since the vast majority of mathematics tutors in America are not trained in teaching conceptual mathematics and having students solve cognitively complex mathematical problems with discussion in order to derive the standard rules and algorithms (Most simply tell students the rule and have students solve problems based upon the rule they just taught the student), their methods are less helpful than in the past for helping struggling students get back up to speed in classes where Common Core mathematics instruction is beginning to take place. Parents need to shop carefully for mathematics tutors. The days of hiring the local mathematics wiz and being able to count on good results have gone. Parents need to ask potential tutors how they teach mathematics and how their instruction has changed in light of the Common Core standards.
Currently, I am providing three mathematics tutorial options using Common Core standards teaching techniques for parents of students grades 5 through 8. I have a fractions tutorial for $25 an hour that you can either schedule through Google Helpouts:
or through my calendar, if you prefer to pay via Paypal: http://meetme.so/laurieflood
For a limited time (until I have three students committed to these and until August), I am also offering free fractions, geometry, and pre-algebra lessons twice weekly for my graduate certificate program. Information on the free, twice weekly lessons are here on Google Helpouts: https://helpouts.google.com/100797727899452785350/ls/95196ccd45123499
In either of the three choices, we will always begin a lesson with a problem that students solve with manipulatives or pictures that help them learn a mathematics rule, formula, or procedure. Then, we will have a discussion about the rule and how the student believes such problems can most efficiently be solved. After I guide students to the most efficient rule or procedure, students will be provided ample opportunity to use the new rule and develop speed and fluency with its use in solving real life problems. I will also incorporate mathematical games and mental mathematics instruction, such as estimation strategies and instruction, in order to help students develop the key skill of checking to see if their answers make sense.
Van de Walle, J. A., Karp, K. S., & Bay-Williams, J. M. (2013). Elementary and middle school mathematics: Teaching developmentally (8th ed.). Upper Saddle River, NJ: Pearson Publication.