One key concept that might be useful in this kind of discussion is "diversity". Others might be "innovation", "ability" and "loophole". (That last being a hint that a close reading of the underlying standards will show a variety of mechanisms aimed at allowing exactly the sort of presentation you are reaching towards. And also that the loudest voices will usually harp on the most ambiguous bits of phrasing.)
But honestly, the primary skill which I think would be most useful in this kind of context is the skill of changing the subject. Arguing about abstractions is futile when each person is reasoning about different underlying experiences. So it's probably best to (a) keep a written list of priorities, so you do not get too lost, and (b) go into the discussion with the aim of listening and finding out about the person's relevant experiences. Once you understand their point, your natural hesitance and thoughtfulness will tend to shine through. Something similar goes on with your students. They are going to need concrete things to hang your concepts onto. And the point of the "fact families" is that they are "worked examples" of concreteness. There's nothing forbidding presentation of abstractions and tools, but you can't do only that any more than you can only present concrete examples. And, frankly, textbook examples tend to get boring - you should also reach for real world examples. Ultimately, the learning has to happen in the minds of your students - it's not something you can do for them. But what you can do is try and tie core concepts to examples that they have some interest in. But a risk here is that quite likely you'll run into cultural issues - getting the wording slightly wrong is sometimes enough to be embarrassing - which might need to be defused with humor or other mechanisms to balance things out. Or, you know, you could yell at them. I hear that that always works - or at least is sometimes not fatal. Thanks, -- Raul On Wed, Jan 14, 2015 at 10:06 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
