I don't think anyone's opposed to looking at function tables; what I see happening in the common core is that they're describing individual basic addition facts, but in a format that makes them serve double purpose as subtraction facts.
If they provide enough time and drills to make sure the children can actually memorize the grammatical facts, that's a good thing. -Wm On Wed, Jan 14, 2015 at 9:28 AM, Roger Hui <[email protected]> wrote: > I have a strong argument for looking at function tables. Show the > following: > > viewmat +/~i.10 > viewmat -/~i.10 > viewmat >./~i.10 > viewmat <./~i.10 > > viewmat 7|+/~i.20 > > And ask questions about symmetries. > > The technique should work for a grade 1 class all the way up to a booth at > the AMS annual conference. (I have done the latter.) > > > > > > On Wed, Jan 14, 2015 at 7:06 AM, Brian Schott <[email protected]> > wrote: > >> First, let me give some background and a warning. The warning is that my >> reason for posting is to get some guidance on the Common Core (CC) pedagogy >> from anyone and this may be the wrong place to ask for it. >> >> The background is that I am a one-or-two-hour-a-week volunteer for a first >> grade class and have absolutely no formal education in education. The >> classroom teacher is in my judgment not trained deeply in CC, and I have no >> expert person to communicate with, although the web contains very detailed >> Statewide CC documents (an example doc link is below). Also, there are a >> handful of web videos showing teachers in their classroom or lecturing on >> CC Math [1,2]. >> >> In a nutshell, I believe that the CC prohibits teachers from teaching or >> even mentioning what we might call in these forums "+ table" and "- table" >> and instead wishes to promote what might be called "mental math" using Fact >> Families! >> >> My question is, how do I manage to convince myself that this CC focus on >> Fact families, not tables, is a natural and effective way to learn math? I >> intend to continue to enthusiastically volunteer as I am doing now, even if >> no one can totally convince me, but I will feel a lot better if I can be >> shown, "the way." >> >> A little more of my research on this subject follows. I apologize for the >> length of this message. >> >> Of one fact, I am quite sure. All fact families are denoted as triplets for >> which the first 2 positive integers sum to the value of the third integer. >> 2,5,7 and 1,5,6 and even 5,5,10 are examples (NB. the first two integers >> may not be different in the case of what I call an "even" fact family, and >> the total may be a 2-digit integer). I am less clear about whether the >> triplets must be expressed as non-decreasing sequences, but they seem to >> always be so. >> >> Another fact, of which I am less sure, is that a fact family can be >> referred to by its largest integer, although that integer does not uniquely >> define a family. So 1,5,6 and 2,4,6 are both fact families of 6. >> >> Less clear to me is whether some fact families are not considered useful, >> or if there is a hierarchy of usefulness. But it is quite clear to me that >> fact families of 10, and to a lesser extent of 5, are most important. Also, >> it seems to me that fact families which include the number 5 as the second >> integer are a little more often used in mental math. >> >> >> >> The following link seems to be pretty clear >> on some aspects of Fact families >> with some examples I will mention. >> Other links at the same domain have been helpful to me, also, although I >> mostly have relied on .pdf, not .doc, files. >> >> https://www.engageny.org/file/1341/download/first-grade-module.doc >> >> For example, that document seems to refer to 2,5,7 as "fact family of 7" . >> >> Ultimately it mentions "fact families of 10" as being the most important >> because of our dependence on the decimal digits system and decimal place >> values used for addition and subtraction. >> >> The following example, also taken from the link above, makes an example >> of >> >> "a >> >> fact family of 5". [You may notice that there may be an error in the >> first sentence, where instead of "the first five fact families," they may >> mean >> " >> the first five fact family," where I believe there are altogether 2 fact >> families of 5: (1 4 5) and (2 3 5).] >> >> >> *********example below************* >> >> "For today’s lesson the teacher will only use the first five fact families, >> for example: >> >> 1 + 4 = 5 >> >> 4 + 1 = 5 >> >> 5 – 4 = 1 >> >> 5 – 1 = 4 >> >> The teacher will demonstrate this using a visual image. >> >> Example: >> >> 1 purple fish swims to meet up with 4 yellow fish. We represent this as: 1 >> + 4 = ? >> >> 4 purple fish swim to meet up with 1 yellow fish. We represent this as: 4 + >> 1 = ? >> >> Once the students get the hang of this, the teacher uses an example where >> the sum from the original fact family is diminished: >> >> 5 fish are together and 1 fish swims away. We represent this as: 5 – 1 = >> ? >> >> 5 fish are together and 4 fish swim away. We represent this as: 5 – 4 = >> ? >> The teacher guides students to use their counting up and counting down >> skills to determine the answers and leads a discussion about why these >> numbers form a family." >> >> *********example above************* >> >> The example has helped me a little to put the Fact families in a >> meaningful >> context >> but I remain skeptical of their use and how to teach them, frankly >> . >> >> Thank you very much, >> >> >> -- >> (B=) <-----my sig >> Brian Schott >> >> [1] https://www.youtube.com/watch?v=twGipANcIqg [long, but great] >> [2] https://www.teachingchannel.org/videos/grade-1-math [shorter, but >> more >> for inspiration] >> ---------------------------------------------------------------------- >> For information about J forums see http://www.jsoftware.com/forums.htm > ---------------------------------------------------------------------- > For information about J forums see http://www.jsoftware.com/forums.htm ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
