Speaking of function tables, I don't think I was instructed how to use them properly. Even as an adult, I don't think I understand them.
I remember being probably about 8 and not being allowed to watch my favorite tv show unless I was able to memorize some multiplication table. I suspect the point is not to memorize a 12x12 table (144 things) but to be able to recognize patterns? Is it meant for reference? We use them on the forums and in J articles. They don't really click for me and even the viewmat examples that Roger posted are perceived as more artistic than helpful in understanding math. On Wed, Jan 14, 2015 at 1:21 PM, William Tanksley, Jr <wtanksle...@gmail.com > wrote: > 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 <rogerhui.can...@gmail.com> > 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 <schott.br...@gmail.com> > > 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 > ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
