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Author Topic: Response to Intervention: Evidenced-based Math Interventions Discussion  (Read 22514 times)
avande
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« Reply #45 on: May 21, 2009, 11:42:47 AM »

By the way, thinking about benchmarks, schools can use their own data over the course of a 1-2 years to set benchmarks for making screening decisions in the future. This not difficult to do and allows the system to set criteria that really serve the needs of the school. All it takes is identifying what is a key outcome that is meaningful in your system. Some systems will pick choose passing the high-stakes test as the outcome they are most concerned about a particular grade level. With the pre-K measures, you might pick something else like success in kindergarten math instruction or success in first grade math instruction. Then you can empirically identify the level of performance at preK in your district that predicted success in K. We are doing these analyses now following a number of preliminary studies evaluating the technical adequacy of the preK probes for screening-type decisions. Here is an excerpt on those data from the manual summarizing where we are so far. What is next for us is to determine what level of performance at preK predicted meeting the benchmark criteria on the K measures (now that we feel pretty solid about the K benchmarks). It just takes a couple of years to sort through it. And the benefit to developing your own benchmarks is that you can continually evaluate their utility and revise over time. I obsess about this type of thing myself and check and double-check criteria on every dataset I collect to be sure those benchmarks hold. I guess I do that because they are the basis for important decisions. When setting your own criteria, you would want to emphasize avoiding false negative errors (since you are making a screening decision) and this will come at a cost of doing more intervention than you might otherwise. This limits the potential for harm so long as intervention is a supplement to general instruction and does not interfere with general ed programming the child would receive.

Screening Utility. Many districts wish to have benchmarks for performance on measures they adopt to assist in determining whether a child’s performance is adequate or whether that student may be at risk for future learning difficulties. Districts and schools are strongly encouraged to establish their own norms and benchmarks for performance, consistent with the tradition of curriculum-based assessment. Given a set of scores on the early numeracy measures and a set of scores obtained on some criterion measure that is meaningful locally, schools can evaluate the degree to which the early numeracy measures correlate with the outcome criteria they care about and what levels of performance on the early numeracy measures meaningfully predict desired learning outcomes. We encourage this type of local evaluation so that districts can evaluate the utility of measures in their own setting and then choose the best measures that will most efficiently aid them in attaining the learning goals that are important in their districts.
Some evidence is available to support the utility of the measures for making decisions about which students require intervention. Performance on the preschool early numeracy measures is significantly higher for kindergarten children than preschool children (18/min on average for preschool children versus 22/min on average for kindergarten children for Choose Number; 7/min on average for preschool children versus 8/min on average for kindergarten children for Count Objects, 19/min on average for preschool children versus 22/min on average for kindergarten children for Rapid Discrimination, and 1.70/second on average for preschool children versus 1.92/second on average for kindergarten children for Free Count). This finding provides evidence that the measures are sensitive to expected performance differences by grade level. Effect sizes ranged from η2  = .13 to .37. Statistically significant differences were also found for most of the measures between scores of children who were enrolled in general education only versus children who were receiving special education services (although some caution is warranted given that the entire sample represented children who were deemed at-risk and were low performing on standardized external measures relative to national normative criteria).
Approximately 40 children were followed from preschool to winter of kindergarten to determine whether scores obtained during the preschool year on the preschool early numeracy measures would correlate with scores obtained on kindergarten curriculum-based measures of early mathematics and literacy. For all of the preschool early numeracy measures, scores obtained in preschool correlated with scores obtained on kindergarten CBMs in the moderate range (correlations ranged from r = .31 to r = .66; Median correlation was r = .46). This predictive validity evidence supports the utility of the preschool early numeracy measures as useful for early detection of possible learning problems.
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klmteach
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« Reply #46 on: May 21, 2009, 03:07:52 PM »

Teaching mathematics at the secondary level can be quite challenging when students bring such diverse bodies of understanding to the classroom.  Are there strategies/interventions general ed teachers can use that are particularly effective at the high school level?  Many thanks!
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kudosorjih
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« Reply #47 on: May 21, 2009, 11:22:00 PM »

I am interested in learning ways to individualized instruction. I don't have a class and I am willing to learn, like you said if one has a system. It's  becomes easier.
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lholdheide
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« Reply #48 on: May 22, 2009, 10:46:53 AM »

Dr. VanDerHeyden and others,

This question came from an email -

"Are there any federal centers or resources available to help SEAs review their math standards and incorporate the math panel recommendations?"
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avande
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« Reply #49 on: May 22, 2009, 11:44:44 AM »

I am interested in learning ways to individualized instruction. I don't have a class and I am willing to learn, like you said if one has a system. It's  becomes easier.

To me, the key to individualizing instruction is having assessment data for a particular student to guide intervention development. There is a body of literature referred to as brief experimental analysis or functional academic assessment. The philosophy underlying these assessment systems is identical to the philosophy underlying functional behavior assessment which might be more familiar to readers. The idea is that you can work briefly with a student to identify intervention features that will accelerate an individual student's learning. The first step is to develop a skill hierarchy (this is usually easily done based on logic--- like fluency with sums to 10 comes before fluency with sums to 12 and application problems like word problems should require computation skills that the student is capable of doing correctly/fluently). Then the idea is to sample back through successively easier skills to identify what the student can and cannot do fluently. Then specific features of an intervention can be tested by providing intervention trials and evaluating the effect on student performance. Commonly tested conditions include reducing task difficulty, providing repeated practice on the task, providing incentives for improved performance. My favorite studies and articles on this topic come from Ed Daly. And my favorite article on this approach appeared in School Psychology Review from 1997 by Daly, Witt, Martens, & Dool. Here is how the intervention becomes individualized via assessment:
- If you provide incentives for performance and performance does not improve, this suggests that a skill-building (rather than motivational) intervention is needed. If performance improves with incentives, then this suggests that contingencies for improved performance are an important feature of successful intervention.
- If you have determined that a skill-building intervention is needed, you might try first reducing task difficulty. If student performance is accurate, but slow, then you would provide intervention to build fluency. Strategies that are effective for doing so include brief uninterrupted intervals of practice with goal setting and incentives for more fluent performance (where fluency is defined as accuracy plus speed, see Binder 1996). If you find that with reduced task difficulty, errors are still prevalent and you have verified that the student can perform the subskills required for successful problem completion, then strategies designed to establish correct responding are in order. These strategies include modeling correct responding, providing examples of both incorrect and correct performance, guided practice where the student response can be interrupted to ensure correct problem completion (immediate corrective feedback), use of prompts and cues to signal correct responding.
- Any hypothesis can be evaluated by collecting baseline data, providing a corrective intervention and evaluating the intervention effect. If you want to be absolutely sure, you can then remove the intervention support and if performance declines again, you have confirmation that the intervention is the right one. For those rare cases where none of the typical manipulations improve performance, you can test idiosyncratic causes for poor performance that you might suspect, like some variable related to the specific task materials or some aspect of the problem presentation. That's what's great about this system, anything you suspect, you can systematically test out in a rapid fashion and know that the intervention will work before you invest the resources to deploy it.
- This is super important because most interventions fail because they are not properly implemented.

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avande
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« Reply #50 on: May 22, 2009, 11:49:12 AM »

NASP hosted an online week-long discussion of can't do/won't do assessment which talks about functional academic assessment. I am not sure if you have to be a member to access (I think you do), but for NASP members, here's the link to the archived event: http://www.nasponline.org/communities/default.aspx?g=topics&f=61
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avande
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« Reply #51 on: May 22, 2009, 12:00:03 PM »

Teaching mathematics at the secondary level can be quite challenging when students bring such diverse bodies of understanding to the classroom.  Are there strategies/interventions general ed teachers can use that are particularly effective at the high school level?  Many thanks!

My hat's off to you! I can very much appreciate how challenging that is. This is why I love to work with younger children, because it just makes so much more sense to put the fence at the edge of the cliff rather than the ambulance at the bottom.... The only good news is that it is easier to show pretty dramatic gains with older students because they have had more time to fall farther behind. I think the first step is to get a handle on where your students are. How deep do the deficits go? The next step is to articulate the essential objectives for current grade-level learning and to monitor progress to make sure you are going to meet that goal. The third step is to prioritize those skills that if you could go back and re-teach to mastery would produce the biggest return for your students (assuming there are deficits). Then carve out 15-20 minutes per day for supplemental intervention to target and repair those skills using classwide intervention. If you could find 30 minutes for supplemental intervention, you could use that time to build fluency with current placement skills too. I was giving a talk last fall and showed a graph where all the students in a 5th grade class performed in the frustrational range on multiplication facts 0-12 (a mid third grade skill). I asked the teachers if they could imagine having to teach factors to those students (which they have to do). I then asked what do you call this pattern of performance and I was looking for the answer, "a classwide learning problem" but a teacher called out, "a tough year!" That was funny but it also really resonated with me because in effect this is what secondary teachers are trying to do. And given the demands of covering the content at their grade level I think there is a tendency to just put your head down and just barrel through it. Some kids get it, and some don't. We are capable of more. We have the science to do better. For my money, it takes having the will to step back and commit to run the marathon. Step back and ask the big question of "do we want to do another year the same way we have in the past and hope for a different outcome?" or do we want to chart a corrective course that will be challenging in the short-term but will eventually take us where we want to go? I always push for the latter. The deficits began accumulating at preK and K, so the solution requires more than a band-aid. It requires a fundamental paradigm shift where LEA and SEA leaders decide to prioritize math learning and allocate resources accordingly. It is foolish (in my opinion) to think that a 50-min block of math instruction will take us where we want to go when most of the nation's 4th and 8th graders are not proficient in the most basic/minimal skills.
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avande
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« Reply #52 on: May 22, 2009, 12:02:38 PM »

Dr. VanDerHeyden and others,

This question came from an email -

"Are there any federal centers or resources available to help SEAs review their math standards and incorporate the math panel recommendations?"

I would like to know if there are. I am not aware of any....
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avande
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« Reply #53 on: May 22, 2009, 12:18:00 PM »

I wonder if the regional resource centers might be helpful in this regard.

It seems pretty straightforward to incorporate the NMP recommendations into state standards. By way of talking points for SEAs, it seems the key implications from the NMP report are to:
- consider paring down the number of skills specified in the state standards (I have assisted districts to do this type of thing with good success-- it's not that difficult to do)
- consider matching each essential skill with an assessment protocol to know whether children in your state are making it or not (with disaggregations)
- consider recommending a minimum core math period that is greater than 50 minutes.
- consider recommending a 20-min supplemental intervention period for schools where 20-50% of students are performing below benchmarks on the essential skills
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doseforum
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« Reply #54 on: September 29, 2009, 02:25:02 AM »

learning new ways to individualized instruction is something good and needed by most instructors.
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rangs987
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« Reply #55 on: October 18, 2009, 05:24:43 AM »

I say make sure you have a strong definition of the problem and then prioritize intervention targets and get started. You can attain remarkable effects in a very short time, but it is a marathon rather than a sprint so you have to anticipate a 2 to 3-year solution. Keep track of the effects you are getting so you know you are using your resources wisely as you go.
Here are the questions I would want to ask:
- are there grade-wide problems? how deep are the deficits in terms of basic foundational, computational skills?
- prioritize 1-2 grade levels where you think you can have good implementation and begin a supplement to the regular math instructional period to re-teach skills that were not mastered (but upon which future growth depends). Run 15 minutes per day of classwide intervention on these skills. Increase difficulty systematically as children show gains.
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« Last Edit: November 14, 2009, 12:41:45 PM by rangs987 » Logged
dgamon22
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« Reply #56 on: October 19, 2009, 11:38:58 PM »

teaching a particular subject on secondary students is pretty tough.
most of them are on the stage where there are lot of things in their mind that tickles their curiosity
and it is also a fact that education is not on the top list.

that makes teaching them, math for example, is not as easy as what you think.
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farhan33
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« Reply #57 on: August 09, 2010, 11:07:02 PM »

Hi All of u ..
Thnx 4 Advice ....
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