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so I'm here with Bill McCollum again and I thought I would love talk about it what we could talk about in this conversation is just the notion I love how the Common Core views algebra in general and then dive deep a little bit into eighth grade because at least as far as I can read the eighth grade standards that in for the Common Core they seem very close to two hours were once thought so this is a very high level but what's your view on that well yeah I would say that be a trade stance campaigning a lot reporting about amber one now algebra 1 soap is not a well-defined time in different states have different schools and administration means different things certain way if you look at the previous Minnesota State Standards I have in common core has a and which other current Minnesota State Fair is become a core has essentially the same decoration is algebra 1 as I stand density and that's mostly in a trade other statement for and and what what the thinking behind because I me when I grow up I think that this is still kinda the normal though there have been some escalation where outer one was you know the standard track was to take that in ninth grade your freshman year in high school up kinda more advanced to take an 8th grade sometimes you hear about investors taking in seventh grade susan is a view to kind of make everyone get on that more advance Trac well I think Common Core tries to strike a middle ground there I think acceleration is offering overtime or starting appropriately for students were not really ready for and where you end up with students come to college gonna be fragile knowledge of a algebra even though they feature the Pacers so from court right there say backs Versailles this no possibility of taking algebra 1 in high school I it's not as if eighth-grade replaces algebra 1 what happens in high school is your revisit a lot of the ideas in greater depth for kids who are very a very advanced they can still badass seconding a revision really just to age bad algebra 1 a.m. eighth-grader um by I think we tried to set a standard should be higher did not push be mathematics so far down in the middle school that you end up with this fight on all in Juno previously middle school was often a bit of a character emigrated from and Charlotte quite understandable that people want to get on to the good stuff AK algebra but now that from or have a lot of really needy mathematics the kids need I'm a very the delving into proportional relationships I love geometry and so in that case I think saving the part about Super 14 eighth-grade that appears in the coming partly because a good middle position there so it's kinda designing that that I have felt I've observed it even appears even with with people that I've I've worked on but can help them to their mathematics is that you know from K through seventh grade typically or even if Griffin on bass track you do a lot of kind of the arithmetic and pre-algebra skills then all the sudden you go to high school in algebra you not you our 12 pre-caucus generate all hits all at once trigonometry and and because as you mention a lot of students and up with a very I call the word Swiss cheese with very proud knowledge they go to college the matter still retake developmental math for college algebra and so this is actually kinda giving more room for algebra so that you hopefully the addition is less fragile that's why we tryna public or we try to build a brand up to algebra a lot of kids hit a wall I'm if I could say well we thought even in kindergarten and first grade when you Booker I reported from that point of euros properties operations explain we call up that may be called property I'm operations and algebraic thinking and in the elementary grades in the Common Core and so that that begins this preparation a great break is really there culminating great where your making sure you're ready for algebraic high school and as I said some kid a rare ready to take out a broad array and I just think there could be a little bit wives about which kids are really ready and and I guess on a similar notion I'm see this affects people's notions of algebra 2 and precalculus per capita the most part is more algebra plus some trigonometry writer and also even geometry to that starts getting touched on as well fairly early on what's your view I mean you do see things are going to change in terms of people for russia's biggest upsets in the same progressions about to run out over to precalculus but there's going to be more conscientious of up kinda love you you hit the nail on the head when a separate chocolates that's not a moral Google+ trigonometry in a perfect world where yeah relearned in the course cold algebra was a really scary thorough knowledge you wouldn't need a forceful the chocolate should be able to go straight to talk to us you have to have trigonometry sure you know a lot of a lot of places algebra 2 has her has a flavor which has created on a tree at every day you have to do that and then just go straight into calculus reason P talk does exist it because kids were not really getting the next 30 understanding about breaking the course is called out over any and so myy I'm years take the course instead you're learning seriously both for great on developing point you and also to students studying hard and time take time it pays to learn the subject matter and then go on to the next subject yeah i know i the focus is a a jumper by just a to other folks on Al derivatives touch on that only the geometry standards in the comic or agenda substantive about a that the core trigonometry in them yes that's right with him which you know and that there is also some stuff about trigonometric functions in the functions writer so that's what I'm hearing is is that between the geometry stands on the album standards are collectively giving you all everything that you need to be college-ready in more advanced courses especially things like calculus but it still is up to the discretion of the school's to understand how to spread it out amongst mocks n years something's going to very fast I get a very strong foundation but the the emphasis is have a strong foundation that's right exactly go response you can know it when still learn that it's the worm subject matter thoroughly and look awesome and and and you know it at the time we have left you know businesses focus on the it good because that is the first real deep exposure to these ideas that we hoped dunes get before they get to college into calculus and you know just looking at the standards and also a conquering as we tried it implement them create exercises for them you know one thing that popped out my there's a lot of focus on really students you know into idiot I have have an intuition for linear relationships grabs and then have taking those ideas a linear relationships and graft in the later leading to ideas have linear functions and function generally that fire that's what a lot of States I a lot of schools and districts for jobless the ball about number one and that's the above the eighth grade algebra is linear relationships when their functions I'm year regimes and 12 variables really getting them your bell yeah I mean just who is this is you know proportional relationship lines is redrawing that connection I linear solving linear equations and pears a simultaneous linear equations so that's kinda good on me D up area than you not only to solving them but really thinking about them and I think there's there are some interesting Congress and the White affix it even construct equations that don't the that have infinite solutions are one solution or yeah a really having their that's really the core of what are students need for many different disciplines that they might be going during college on the high school standards go further if the exponential functions operatic productions but getting to linear I for understanding as we near racial even when he approached things down is is an important component above college readiness and this idea functions which i think our almost every student you know that when they first see it usually it may be laid out a row on algebra 2 like okay you know an hour why did stuff like writing wise equal to a 3x plus five and now he is the Messiah me to write this is equal to three experts 5 it looks kinda like an arbitrary a notational change without an appreciation of what a a function that is really all about Julia mapping between sets and it looks like the Concours really trying to make sure people get the Muni well function well that's true although that's not actually required for the high school standards in a trade it's not required students learning the formal fighting notation partly for the reasons you just K it becomes a notational distraction kids don't even understand why they're doing it if you start out saying let's understand a fraction as a thing as a rule that pics inputs and outputs which could be. expressed using equation but the stakes of making up what a function is very I you then you don't get distracted by the notational King James I can come later when she is not there object solemnly a one soon understand they're looking where then it doesn't seem strange to lose you the letter at for that day rights is really get the idea of a function before we see this and then and then you can understand what you the notation starts to make more sense are kinda putting the input inside the box and the dryer outputting or this is this is this is the definition of what the boxes and the little output a yeah I think in some left over at the new math maybe that functions but come I'm and obsessive concern too early in the curriculum I so I think you can go a lot of work with linear functions you got going through obsessed about the notation but getting the idea here up a only a fraction and certain nonlinear functions be used to model relationships between Gary gonna be because I didn't want quality depends on the other you got an independent variable dependent variable and then the formalities can come later right adding that modeling point is another thing that you definitely see the Common Core really emphasizes the say taking you know real hopefully close to real world situations and actually trying to actual model as opposed to just you know get automatic way should resolve it yeah molly is a very important concerning their Concord generally it really comes to reach fruition in high school wary there's a whole system modeling standards indicated by that modeling star and he didn't expect it to be able to put to use in mathematics save water drink inning a working with problems rock on mathematics no yeah now this is very helpful that thanks so much bill sure