I went to Canvas (Instructure’s online course platform that has a “free for teachers” option) thinking — this can be the platform (as well as D2L because that’s what my institution uses). The wild dream is that people would use it enough for Canvas to imagine this is a good idea as a gateway drug.
OF course, the huge huge huge issues are all those “little” problems w/ Canvas, but that can be ameliorated by designing the course so it *doesn’t* have to be done online; it can be a “teacher resource.”
I found my link to a Scottsdale Basic Arithmetic course. Active course dates: Active Course Dates: Feb 4, 2013 – May 3, 2013…. so was it a one-off? Why? (Possibly because, it seems, it spends about five minutes on each thing as a “quick procedural review.” The structures and support, though, seem pretty excellent.)
The nice thing is this class has like all kinds of organizational STUFF. It’s got a stealable skeleton.
I looked up the college and … no, it’s not a one-off. They still teach Basic ARithmetic –which led me to *another* workbook with yes! visuals … but not with the structure and practice … and yes, I need to stop questioning whether I should do this (has it been done already? Is the other stuff good enough?) and … get back to it
]]>Yesterday I inspired two outbursts of giggles…. which don’t convey in text (“you had to be there” )but … I swear thigns like Twitter Math Camp have improved my delivery in late Friday afternoon working with the exhausted.
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Many will apply the distributive property that they recently learned.
Then, “Oh, no!!! I did it wrong! We have to do what’s in the parentheses first!”
I do try to make the connections but it *almost* makes me wish I were the teacher teacher … and could take steps to cement the connection.
]]>Part 1 Part 2 Part 3 Part 4 Part 5
From
The National Center on Education and the Economy (NCEE) asked: What does it really mean to be college and work ready? They conducted a two-and-a-half year study to try to answer that question. What they discovered is most of the math that is required of students before beginning college courses and the math that most enables students to be successful in college courses is not high school mathematics, but middle school mathematics. Ratio, proportion, expressions and simple equations, and arithmetic were especially important (NCEE, 2013).
In other words, if we could help our students develop strong math skills at levels A through C/D in the CCR, they would be well-prepared to tackle college level classes or even ready to succeed in training required at the workplace.
Arithmetic, ratio, proportions, expressions and simmple equations, people.
If students *actually understand* that, they can get past those barriers.
Here’s my thinking: Some students do, in the assorted “accelerated reforms,” organize exactly those concepts and they’re in that still-too-small group that succeeds at the “college level” stats courses. What if we actually taught those concepts in an adult context? That article goes on to give examples of mixing the “level A” with the C and D. When you’re doing fun things with arithmetic, you can include things like halves… maybe even quarters. 50% and 0.5 and a half should be understood as synonymous.
And has it been done?
Dorothea Steinke put together a curriculum starting with the concepts of “parts and wholes” — that when we can figure out whether we’re looking for a whole and we know the parts… or whether we know the whole and are figuring out a part… that this is what math is built on. She also includes lots of concrete, multisensory activities to build understanding.
Results? ” “…the West Side Learning Lab of the Community College of Denver, CO, has seen 92 percent (48 of 52) of its GED students pass the GED math test on the first try. ”
So….
I want to scale this up.
I want to open this up.
There aren’t many people who understand the math *and* understand how to help people get there. (Here’s my almost-up-to-date “about me” ).
Can we get together?
Can we open this even *wider*? Can we make this so the myriad folks who think they just can’t grasp math at all… but who might just take a chance… could learn how to think with numbers, and do stuff with numbers in their lives?
Can we make cognitively accessible math? (An example of making a percent problem cognitively accessible is here ).
If you’re even remotely interested in this, join us at Rebus Community. Big ideas have to start with … small ideas, right?
…. now I need to get back to making the little pieces I *can* do by myself… between students…
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This is part 5 of a summary of research and articles about remedial/developmental math in colleges and adult education.
What would I like to see happen? What would I be willing to invest my time and energy and knowledge in?
Remember this?
In particular, we are interested in exploring the hypothesis that these students who have failed to learn mathematics in a deep and lasting way up to this point might be able to do so if we can convince them, first, that mathematics makes sense, and then provide them with the tools and opportunities to think and reason.
Yes, this has been tried!
This author observed math classrooms at two schools. Each was making major efforts to improve student outcomes for developmental math. Both schools provided lots of support and advising, and dedicated enthusiastic instructors.
One school kept the traditional textbook and “remedial pedagogy” with structured procedural practice. The other brought in instructors who focused on students’ developing meaning and making connections between their intuitions and the mathematics.
The second school had much better results.
Yes, small sample size… but both schools were Trying New Things They Believed In and, yes, student attitudes shifted in positive directions.
The teaching was fundamentally different though, with the “conceptual” schools making lots of “real life” connections and building from cognitive models the students already had. So, for integer lessons, the “rules” classroom had clear explanations and practice with rules and patterns… the “concepts” class started with temperature data from different cities.
And… ponder this from the conclusion — I could only get access to “full text HTML” unformatted text so I’ve added white space:
From this perspective, the two classrooms at College X serve as a profound existence proof: There is an alternative to the default “remedial” pedagogy that dominates developmental math classrooms,…
The fundamental differences between “remedial” pedagogy and an instructional approach that reflects math educators’ formal recommendations for developing mathematical proficiency are not necessarily glaringly obvious when the vantage point is located outside of the classroom.
… adding resources to or amending the structure of a developmental math course does not, by itself, affect the nature of instructional practice enacted within the course.
Given the persistent dominance of the default “remedial” pedagogy across developmental math classrooms, tinkering at the margins of instructional practice holds little promise.
In the absence of sustained attention to what actually unfolds inside developmental math classrooms, such efforts at reform may perpetuate similarly dismal outcomes to pre-reform levels.
As Hinds (2011) aptly notes, “Rather than addressing the instructional methods that dominate remedial math classrooms and the cultural and systemic factors that keep those methods in place, . . . the most popular reform efforts actually sidestep the critical issue of teaching practice” (p. 23).
So…. given that, what do we need to change? What should we be teaching?
From
This is about the assorted courses to prepare students for High School Equivalency (HSE) tests.
“Some educators choose to prepare learners for the HSE test by spending hours practicing sample questions from test prep books. While familiarity with the types of test questions can be helpful, learners do not come away with much understanding of the mathematical content and thus are less likely to be successful on the HSE assessment or any additional assessments used for entry or placement purposes for certification programs or further education. Better preparation for the HSE might be to delve deeply into the mathematical concepts and procedures, particularly addressing algebra. “
And from another article in that issue featuring numeracy
Unfortunately, too many teachers feel like they don’t have the time to give students the foundation that would allow their students to actually understand what is being taught. They may teach students procedures and tricks, hoping that they will retain those procedures long enough to at least pass the test.
However, without foundational understanding, students rarely remember those procedures…As a result, teachers reteach the same procedures over and over again, rarely successfully getting their students to understand when to use those procedures. According to Givvin, Stigler, and Thompson (2011):
Without conceptual supports and without a strong rote memory, the rules, procedures, and notations they had been taught started to degrade and get buggy over time. The process was exacerbated by an ever-increasing collection of disconnected facts to remember.
This has been your erstwhile blogger’s experience in K-12 education: as students went from year to year, they’d start at arithmetic because the students didn’t really understand it and… move faster and faster through the procedures because there was so much to catch up to and it is *EVER SO IMPORTANT* to say they are “doing grade level work.” If they’re memorizing to survive, that’s not really that grade level work.
I’m going to make this its own “part” because it deserves a big drum rolll… so posting this much now…
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So… how can courses be improved? Some ideas:
Saxon D, Martirosyan N. NADE Members Respond: Improving Accelerated Developmental Mathematics Courses. Journal Of Developmental Education [serial online]. Fall2017 2017;41(1):24-27
The top 3 challenges to running “supported accelerated courses” which happen to be really consistent with students not understanding the math:
… and… what do the teachers doing these courses say? Remember the caveat earlier about recognizing that faculty do think some students need more time and more remediation. Also, from
Cafarella B. Acceleration and Compression in Developmental Mathematics: Faculty Viewpoints. Journal Of Developmental Education [serial online]. Winter2016 2016;39(2):12-25.
And the student attitudes?
This was the real icing on the cake for me.
Benken, B. M., Ramirez, J., Xuhui, L., & Wetendorf, S. (2015). Developmental Mathematics Success: Impact of Students’ Knowledge and Attitudes. Journal Of Developmental Education, 38(2), 14-31.
This study attempted to create a “detailed picture” of developmental math students “both in terms of their mathematical preparation and affect.”
While it stated that pre-college courses needed to address conceptual and procedural knowledge, it didn’t address whether this actually happened in the courses.
Pre- and post- course surveys about attitudes were administered.
The most “extremely significant” change in attitude?
Increase in the opinion that some people have a knack for mathematics and some don’t.
Since students didn’t increase in liking math, I can hazard a pretty safe guess where they think they fall in that categorization.
Next: what can be done???? who’s doing it???
]]>So: what is the current state of developmental education? According to Hunter Boylan:
“If the only thing that you are offering your students is a course in pre-algebra, then it is probably a remedial course. If you are offering a course in pre-algebra that is supported by counseling, tutoring, and advising, where the course is taught according to principles of how adults learn and develop then that is a developmental course. I often say that we don’t know whether developmental education works or not. Most institutions haven’t tried it yet.” (emphasis added)
Levine-Brown P, Anthony S. The Current State of Developmental Education: An Interview with Hunter R. Boylan. Journal Of Developmental Education [serial online]. Fall2017 2017;41(1):18-22
(Obvious to me: adults learn and develop when the content is somewhere near their zone of proximal development or, in less technical terms, if it’s content that they have the background knowledge necessary for understanding.)
Next tweet:
Another article questioning the actual value of developmental math.
Quarles C, Davis M. Is Learning in Developmental Math Associated With Community College Outcomes?. Community College Review [serial online]. January 2017;45(1):33.
“ Results: After controlling for grades in previous classes, procedural algebra skills were not associated with higher grades in college-level math. Conceptual mathematics proficiency was associated with higher grades in general education math but not in precalculus. In developmental classes, however, learning gains were primarily procedural, which were correlated with grades…Instruction focused on procedural skills may not be preparing students for college mathematics.
This article at least recognizes that developmental math is generally taught procedurally. It didn’t, to my disappointment, explore the value of actually *teaching* concepts.
Next tweet:
No, since things aren’t working: why not just speed it up and add help and support.
An article exploring interventions across Texas:
Weisburst E, Daugherty L, Miller T, Martorell P, Cossairt J. Innovative Pathways Through Developmental Education and Postsecondary Success: An Examination of Developmental Math Interventions Across Texas. Journal Of Higher Education [serial online]. March 2017;88(2):183-209.
Things look reasonably good:
The relationship between both interventions and student outcomes was generally positive. …students in this intervention had approximately 4% higher DE math pass rates in their initial DE math course in their first semester, 1% higher propensities to take and pass an FCL math course within a year, 4% higher persistence for the 1st year of study, and 2% higher persistence to the 2nd year of study. “
Total increase: …” Students in DE student success courses had 7.5% higher DE math pass rates, 12% higher 1-year FCL enrollment, 12% higher 1-year FCL pass rates, and 9.5% (8%) higher 1 (2)-year persistence rates. These results are particularly striking given that the population of students in DE student success courses had lower college readiness prior to enrolling in the intervention.
Also, this:
…Relative to similar students not enrolled in short DE math courses, these students were 12% more likely to pass their DE math course (24% above mean pass rates), and they were 2% more likely to take and pass an FCL math course within a year (33% above mean enrollment rates and 36% above mean pass rates). …However, students in these courses had 0.7% higher 2-year graduation rates (37% greater than mean graduation rates).
That seems good but… looking at the statistics closely:
Despite the nice sounding relative increases… 7.8 % of students who took the success course went on to pass a “first college level” math course, vs. 7.5% who didn’t take the course.
92.2% of the students still failed.
The relative decrease in failure — 0.43%.
I remembered this and realized it hadn’t made the tweetstorm (or Powerpoint), and added it.
Better results from California:
Hern K, Snell M. The California Acceleration Project: Reforming Developmental Education to Increase Student Completion of College-Level Math and English. New Directions For Community Colleges[serial online]. Fall2014 2014;2014(167):27-39.
Before:
6% of students beginning 3 or more levels below college math go on to complete a college level math course.
More than half of all Black and Latino community college students place there
Acceleration w/ support “far exceeded goals” – 4.5 times as likely to succeed.
Still, none of the success rates were above 40%.
Another “reform approach: Do we even need the algebra?
Three Year Effects of Corequisite Remediation with College Level Statistics/
“More successful” was 56% passing the Stats course vs. 39% passing the “remedial algebra” course.
Students with Arithmetic placement were not included. What about them?
Here’s one more “successful” path:
Fong K, Melguizo T, Prather G. Increasing Success Rates in Developmental Math: The Complementary Role of Individual and Institutional Characteristics. Research In Higher Education [serial online]. November 2015;56(7):719-749.
Of course, if you apply your business math “chain discount” math to this, you discern that from the Arithmetic level, 6.6% of students pass a gateway course; from Pre-algebra, 11.7%; from Elementary Algebra, 27.6% and from INtermediate Algebra, 54.3%.
The article didn’t provide those stats.
This is big enough already… end of Part 3.
]]>Part 2 of a summary of research (including some summaries of research :)) about mathematics and adult education and developmental / remedial math in colleges.
Stigler, J.W. et al. (2010) What community college developmental mathematics students understand about mathematics. MathAMATYC Educ. 10, 4–16
This article is full full full of interviews and information about what students *understand* about math. Here’s a little table w/ the questions most missed and the mistakes they made.
Some patterns:
The big one, to me:
Perhaps my favorite paragraphs:
Currently there is great interest in reforming developmental mathematics education at the community college. Yet, it is worth noting that almost none of the reforms have focused on actually changing the teaching methods and routines that define the teaching and learning of mathematics in community colleges.
In particular, we are interested in exploring the hypothesis that these students who have failed to learn mathematics in a deep and lasting way up to this point might be able to do so if we can convince them, first, that mathematics makes sense, and then provide them with the tools and opportunities to think and reason.
Let me propose the radical idea that this shouldn’t be limited to students who fail by a little bit. This should include students who are coming in with the lowest standing… especially since this tends to be marginalized and/or minority students.
Okay, Part 3 is: what is the current state of developmental education — but I’ve about used up my time allotted for this.
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Yesterday I posted a “thread” on twitter — my first attempt at that as communication.
I’m going to try to replicate that here, more accessibly than the images of powerpoint slides.
I’ve been reading a lot of research on developmental math, remedial math, and adult ed math. Sometimes I’ve blogged about an individual article. It’s tme to summarize.
I noticed that research that wasn’t even about the same kinds of things had some common phenomena.
HEre goes the thread, more verbally:
There are lots of books and articles about our nationwide problem with understanding math. Marilyn Burns’ _Math: Facing an American Phobia_, Innumeracy: Mathematical Illiteracy and Its Consequences are just two.
What is actually happening in the postsecondary scene?
This article is one of many scathing analyses of remedial math in colleges. So few people succeed in it that we should dump it and put people in college level classes with support.
It notes: “best practices have demonstrated that as many as half of all current remedial students can succeed this way.”
The rest of them? Oh, there are nice vocational programs that don’t require math. (No, they can’t tell us where they are.)
Next tweet
Why are the students unsuccessful? Well, several articles have a laundry list.
From
Cafarella B. Developmental Math: What’s the Answer?. Community College Enterprise [serial online]. Spring2016 2016;22(1):55-67
we have
Note that none of these are the responsibility of schools. It’s on the student. Note also that poor attendance and apathy are likely “side effects” of “extreme underpreparedness,” otherwise known as not knowing the basics of math.
Next tweet:
From the adult ed community,
Showalter D, Wollett C, Reynolds S. Teaching a High-Level Contextualized Mathematics Curriculum to Adult Basic Learners. Journal Of Research & Practice For Adult Literacy, Secondary & Basic Education [serial online]. Summer2014 2014;3(2):21.
Again… they don’t know the math.
Back to college, from
Zientek L, Schneider C, Onwuegbuzie A. Instructors’ Perceptions About Student Success and Placement in Developmental Mathematics Courses. Community College Enterprise [serial online]. Spring2014 2014;20(1):67-84.
:
“Lack of basic math skills” … and “time delay” — which in my experience is usually “I didn’t get it the first time either” are the *overwhelmingly* most common answers. The surveyers did not include lack of aptitude or “some people just can’t do math” as answers to be included, but it would have been interesting to see how many teachers had that attitude.
From an interview with Paul Nolting
Boylan H. Improving Success in Developmental Mathematics: An Interview with Paul Nolting. Journal Of Developmental Education[serial online]. Spring2011 2011;34(3):20-27.
“High school math grading systems can measure algebra skills, but they are also often a measure of effort and extra credit as an indicator of success, compared to the placement test which measures only pure alebra knowledge.”
Now, one could argue about how well the tests do that but his point that grades can be inflated is painfully valid.
I’ll pause here because the next slides are about the Stigler, et al article which dives into exactly what students *understand* about the math.
]]>No, this isn’t OER. Students are paying big bucks to be beta testers. Sorry, I’m not going to pretend to like it.
Now, I wouldn’t like it any more if it were free. Sorry, “oh, quality! it’s all relative! We do as well as non OER so it’s good enough!” is bogus. Guess which particular students will be able to work around those little errors? Hint: it’s not random. Granted, if it were OER, I could edit it.
That said, they do a pretty darned good progression in the lessons on the new stuff, which is stats. They ask appropriate “obvious” questions before getting to the interpretive stuff. They “show example” part almost always works…
…. and one of my most “just tell me what to sya!” students was going to do that but … then they *did* actually see something in the patterns to tlak about THey had figured out that if the perimeter of a rectangular something (I don’t remember what but it was a real something) was 36 feet and the width was 6, then the length had to be 12. They were to use natural numbers to figure out the other combinations.
Most assignments just stop with “figure out the length” and they do the formula and okay, fine.
Nope, first they had to find the other combinations with natural numbers that would get that perimeter.
*Then* they used Excel to sort the length from small to big and … observe.
Student honestly thought it was all kinds of cool how one went up and one went down. They hadn’t been asked to notice things about the area but … they put it in (hey, it’s “fill down”) and noticed … hey, the middle one is 36 and then it’s matched pairs working out and “oh, cool!!”
Now, we need to make the ratio of cool to crying just a whole lot better, people.
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