Reviewing Two Recent Studies of Math Deficient Students
[CLICK
HERE for the Full Blog Message]
Introduction
Two Blog messages ago (on September 28th), I
began a two-part discussion on:
Closing Academic Gaps in Middle and
High School: When Students Enroll
without Mastering Elementary Prerequisites (Part I)
The MTSS Dilemma—Differentiate at the
Grade Level or Remediate at the Student Skill Level?
While I usually publish two-part
messages back-to-back, my October interview with Education Talk Radio
host Larry Jacobs on:
The Traps and Troubles with “Trauma-Informed”
Schools: Most Approaches Are Not Scientifically-Based,
Field-Tested, Validated, or Multi-Tiered
was too time-sensitive to delay even a few weeks.
[CLICK
HERE for the related Full Blog Message on how to implement effective
science-to-practice Trauma Sensitive schools]
. . . But now we’re back on track.
_ _ _ _ _
_ _ _ _ _
In this Blog (Part
II), we will briefly:·
- Revisit our Part I discussion of how secondary schools currently do and (recommended) should address students who enter with academic skills so low that they can’t conceivably succeed in grade-level coursework; and then
- Review and apply the results of two important and topic-relevant research studies, one published in 2018—but referenced in a the74 Million article about a month ago, and another published this Fall by New Classrooms that addresses the results and implications of district, state, and federal policies that suggest—or even require—teachers to focus on grade-level standards regardless of their difficulty or their students’ mastery of the prerequisite skills that predict successful learning and advancement.
_ _ _ _ _ _ _ _ _ _ _
Revisiting the Secondary-Level MTSS Dilemma: When Students “Rise-Up” without Mastering Elementary- or Readiness-Level
Prerequisites
In Part I, we
discussed a common middle and high school pedagogical problem that occurs when students transition in (or up), and they
haven’t mastered the prerequisite academic skills to succeed at the next grade
level.
While this occurs most often in the areas of
English, reading, and literacy, or mathematics, calculation, and numeracy, we
sometimes forget the impact on students’ learning when they are also unprepared
to effectively write or communicate verbally at their grade levels.
And then there are the “lateral effects”
when students’ low literacy or mathematics skills negatively impact their
learning and performance in science, the social sciences, or in other
transdisciplinary areas.
Typically, when students’ prerequisite
academic skills are so low that everyone knows that they have virtually no
chance of passing the next middle or high school course, most schools use one
of the following Options:
· Option 1.
Schools schedule the “not-ready-for-prime-time” students into their
existing course sequences, and teach them at their grade levels—hoping that
effective differentiated instruction will close the existing achievement
gaps at the same time that the students learn and master the new,
course-related content and skills.
_ _ _ _ _
· Option 2.
Schools use Option 1—scheduling the “not-ready-for-prime-time”
students into their existing course sequences, and then they offer/provide
tutors or tutoring (usually before or after school) to supplement the
instruction and “close” the gaps.
_ _ _ _ _
· Option 3.
Schools “double-block” the students—scheduling them into the existing
course sequences while also giving them an additional academic period a day (or
less) to remediate their skills gaps.
_ _ _ _ _
· Option 4.
Schools “double-block” the students, but the students have the same
teacher for both blocks. This allows
the teacher to follow the grade-level course’s syllabus, but s/he can spend
time remediating students’ prerequisite skills gaps and adapting the instruction
so they are prepared for and can learn and master the grade-level course
material.
_ _ _ _ _
The Part I discussion emphasized the
importance of completing, for all students with significant academic skill
gaps, a data-based problem-solving process—including diagnostic assessments
to determine the depth, breadth, and root causes of the gaps—so that needed
services, supports, instructional strategies, and interventions are accurately
identified.
While we understand the time, effort, and
good intentions of our school colleagues, we still noted that:
Unfortunately, many
schools have some data, but it is descriptive and not diagnostic data. And then they use these data to inadvertently
play “intervention roulette”—throwing “interventions” at problems without
really knowing the root causes as to why they exist.
To demonstrate the benefits of the
recommended diagnostic assessment, data-based problem-solving process, we also
noted that:
In reality, based on
their data-based student analyses, schools may be well-advised to have Options
1, 3, and 4 available in order to maximize the learning and mastery of
different students with different learning histories and instructional needs.
For example, while Option 2—Tutoring
can be effective for students with narrow skill gaps, these Options will not
work for students with significant academic skill gaps.
[For Option 3, obviously, schools
need to coordinate the curriculum, instruction, and interventions in order to
attain the strongest student outcomes.]
_ _ _ _ _
The Part I discussion then differentiated
between middle schools versus high schools that have students with critical
academic skill gaps.
Here we noted that middle schools (if they
choose to take it) have more flexibility to “individualize” their students,
staff, and courses than high schools—especially when the latter are not allowed
(usually, by their state education codes) to give course credit for “remedial”
courses. This helps deliver the targeted
interventions that students with significant skill gaps need.
Indeed, we recommended that middle schools,
if they know the academic and behavioral status of their rising 6th graders in
April or May (an implicit recommendation), they can align their students,
staff, and courses to flexibly meet the needs of different clusters of
students—from those entering with significant academic skill gaps, to those
whose academic skills already exceed the 6th grade courses they might “repeat.”
We concluded that, if middle school
students with significant academic skill gaps “pass” their courses, but do not
master the “elementary” and “middle school” skills that they need, we
have simply passed the “problem” on to the high school “to solve.”
_ _ _ _ _
At the high school level, we described a
number of “stark realities” (please see the original post). These led up to an Option 5 that we
said—under explicit conditions—should be allowed, if not encouraged, by every
state department of education and the U.S. Department of Education.
Option 5 is for students who have
no chance of passing their next middle or high school course even using Options
1, 3, or 4 above—because their prerequisite academic skills are so
low. This appraisal is based on
objective, multi-instrument, diagnostic skill gap analyses of each struggling
student—conducted at the relevant secondary school level.
Option 5
involves scheduling students into a course (or a double-blocked course) in
their academic area(s) of deficiency that targets its focus and instruction
on the students’ functional, instructional skill level. That is, the course takes students from their
lowest points of skill mastery (regardless of level), and moves them flexibly
through each grade level’s scope and sequence as quickly as they can master and
apply the material.
This should
be an instructional—not a credit recovery or
computer/software-dependent—course with a teacher qualified both in
instruction and intervention.
Moreover,
this is the students’ only course in the targeted academic area, and the course
instructors are responsible for making the content and materials relevant to
the grade level of the student, even as they are teaching specific academic
skills at the students’ current functional skill levels.
Thus,
students are not concurrently taking a grade-level course in the same
academic area (as in Options 1 through 4 above). In addition, the teachers in these students’
science, social science, or other courses also know the students’ current
functional skill levels—differentiating their instruction as needed, while
providing additional supports, so that the students’ areas of academic weakness
do not negatively impact their learning in these “lateral” courses.
_ _ _ _ _
Possible Student
Candidates for Option 5. Part I of
this Series discussed the possible (combination of) reasons why
rising-secondary students transition
from elementary to middle school—or middle school to high school—without the
prerequisite academic skills to succeed at the next grade level.
For students with significant academic
skill and mastery gaps at the secondary level, the most common root causes described
were:
· There were
significant instructional gaps during the student’s educational history such
that the student did not have the opportunity to learn and master essential academic
skills.
This includes, for
example, students who were (a) home-schooled, (b) had new teachers who were
unprepared to teach, (c) had long-term substitute or out-of-field teachers for
lengthy periods of time, or (d) were in classrooms with too many different
student skill groups for the teachers to effectively teach.
_ _ _ _ _
· There were
significant curricular gaps during the student’s educational history such that
the student did not have the opportunity to learn and master essential academic
skills.
This includes, for
example, (a) schools without the appropriate evidence-based curricula or
curricular materials to support teachers’ goals of effectively differentiating
instruction; (b) schools where teachers—at the same grade level—were teaching
the same content but with different algorithms, rubrics, or skill scripts that
were then not reinforced by the next year’s teachers—especially as they
“inherited” a mix of students who were taught specific skills in vastly
different ways; or (c) schools that adopted grade-level curricula that were not
aligned with state academic standards, and that did not articulate with the
curricular expectations at the next grade level.
_ _ _ _ _
· The schools, attended
by the student during his/her educational history, had an absent, inadequate,
or ineffective multi-tiered system of supports that did not address his or her
academic needs.
_ _ _ _ _
· The student was taught, over a long or significant
period of time, in a school or classroom where the relationships or climates were
so negative (or negatively perceived by him/her) that they impacted his/her
long-term academic engagement, motivation, attendance, and access or ability to
learn.
_ _ _ _ _
· The student had known or has newly-diagnosed (due to
the root cause analysis) biological, physiological, biochemical, neurological,
or other physically- or medically-related conditions or factors that
significantly impacted his or her learning and mastery, or the speed that s/he
learns and masters new skills.
_ _ _ _ _
· The student had (and may still have) frequent or
significant personal, familial, or other traumatic life events or crises that
impacted his or her academic engagement, motivation, attendance, and access or
ability to learn.
_ _ _ _ _
· The student’s skill gaps created such a level of
frustration that the resulting social, emotional, or behavioral reactions by
the student (along an “acting out” to “checking out” continuum) overshadowed
the original and present academic concerns—resulting in the absence of (or the
student’s avoidance of) needed services or supports.
_ _ _ _ _
We concluded that the
vast majority of these root causes point to the fact that students who will
most benefit from Option 5 are students who did not have the opportunity to
originally learn and master the academic skills that are now embedded in their
significant skill gap.
At the same time, we
emphasized that many of these student will need additional social, emotional,
or behavioral services and supports so that the academic interventions can be
successful. . . and that their motivation and positive, active engagement in
the Option 5 course(s) and classroom will be a key factor in determining
success.
This is especially
true at the high school level, when students are confronted with the reality of
a four-plus year high school career (which—from an adolescent’s perspective—may
look worse than dropping out, or going for a GED).
_ _ _ _ _ _ _ _ _ _
Connecting Root
Cause Analyses with a Continuum of Academic Supports and Interventions. Finally, in Part I, we emphasized that:
Option 5
will only succeed if the best services, supports, strategies, and interventions
are matched to the root causes that explain why secondary students have such
significant academic skill gaps.
Expanding on this
discussion, we described the key components of our Positive Academic
Supports and Services (PASS) continuum. . . a science-to-practice blueprint
that, in the context of the current discussion, is tailored to each individual student’s
needs (see the Figure below).
_ _ _ _ _ _ _ _ _
Validating the Magnitude of the Problem for Students
with Significant Skill Gaps
To the continue the
discussion begun in Part I, we are now going to focus on the impact and
implications when students have significant skill gaps in mathematics at
the secondary level.
Pedagogically, and
in contrast to literacy, math tends to be more finite (i.e., there are right
and wrong answers), more dependent on specific mathematical algorithms (e.g.,
formulae or clear problem-solving steps), and more sequentially scaffolded—with
certain skills laying the “foundation” as prerequisite skills to a next set of
skills. Thus, math is a perfect area to
investigate the “impact and implications” noted above.
In a the74 article
published on September 24, 2019, Joel Rose the CEO of New Classroom
Innovation Partners, and Daniel Weisberg the CEO of TNTP—organizations
that both focus on helping schools to address the needs of underachieving students—discussed
their work with students with significant skill gaps in mathematics.
[CLICK
HERE for the74 article, “Do Kids Fall Behind in Math Because There Isn’t
Enough Grade-level Material, or Because There’s Too Much? It’s Both”]
Citing a 2018 TNTP
Report, “The Opportunity Myth,” they stated that this Report found:
when students don’t meet grade-level standards, the
problem usually isn’t that they tried and failed but that they were never given
a real chance to try in the first place. The 4,000 students TNTP studied across
five school systems spent hundreds of hours each year on work that was below their
grade level. Those who started the year behind academically were the least
likely to have grade-appropriate assignments—even when they were capable of
succeeding on them—making it nearly impossible for them to ever catch up to
their peers.
In essence, Rose
and Weisberg are talking about (what we call) Instructional or Curricular
Casualties.
These are students
who “rise up” to middle or high school with significant skill gaps because of (a)
the poor quality of previous mathematical instruction; (b) the poor quality of
the progress monitoring, early intervention, or intensive intervention systems;
(c) the poor selection or design of effective curricular lessons and materials in
math; and/or (d) the poor sequencing or scaffolding of the math curriculum—including
providing students opportunities for massed, distributed, and applied practice.
Critically, Instructional
or Curricular Casualty Students can learn, they just have not had the
sustained opportunity to learn.
_ _ _ _ _
This is in contrast
to students who have legitimate difficulty learning and independently mastering
their mathematical skills—even in the face of good, differentiated instruction,
and well-designed and implemented curricular materials. While a small number of these students may
have a specific learning disability in math, the vast majority need more
strategic instruction a different instructional approach, smaller learning and
mastery “chunks,” higher ratios of known to unknown material, and more positive
practice repetitions relative to memorization and automatic recall or
application.
_ _ _ _ _
Regardless of why a
student has a significant skill gap in mathematics, the impact and implications
are notable.
In their the74
article, Rose and Weisberg reproduced a figure (see below) from a 2012 ACT
report that longitudinally analyzed tens of thousands of students who were
behind in math in fourth versus eighth grade, respectively. The goal was to identify—from a normative
perspective—how many students academically
“caught up” over a four-year period of time.
As is evident in
the figure:
·
Students who began 4th grade “at grade level,”
had an 82% probability of being on grade level in 8th grade—four years later.
·
Students who began 8th grade “at grade level,”
had an 70% probability of being on grade level in 12th grade—four years later.
·
Students who began 4th grade “off track,” had an
46% probability of being on grade level in 8th grade—four years later.
·
Students who began 8th grade “off track,” had an
19% probability of being on grade level in 12th grade—four years later.
·
Students who began 4th grade “far off track,”
had an 10% probability of being on grade level in 8th grade—four years later.
·
Students who began 8th grade “far off track,”
had an 3% probability of being on grade level in 12th grade—four years later
From the Report, it
appears that most of the (especially) “far off track” students were receiving
Options 1 through Option 4 above. This Report
and these data simply reinforce that these Options have a low probability of
significantly improving the learning, mastery, and math proficiency of students
with significant skill gaps—in both middle and high school.
This, at least, puts
the consideration of Option 5 “on the table”—once again, in the context of both
root cause analyses and multi-tiered systems of support.
_ _ _ _ _ _ _ _ _ _
The Iceberg Problem in Mathematics: How Policies, Practices, and Resources
Limit Option 5
Rose and Weisberg’s
the74 article goes on to reference a September 2019 Report released by Rose’s
New Classroom Innovation Partners:
“The Iceberg Problem: How Assessment and Accountability
Policies Cause Learning Gaps in Math to Persist Below the Surface . . . and
What to Do About It”
[CLICK HERE
for Report]
I encourage everyone
to read this 75-page Report which provides compelling information on (a) how
different math skills are scaffolded across most mathematics curricula; and (b)
the cumulative (negative) effects that occur when students fall significantly
behind in their learning and mastery of previous, now-prerequisite skills—and yet,
they are scheduled into courses that teach at their current grade level.
Below are the four “Key
Insights” from Report—conclusions that support the primary theses of this
two-part Blog Series.
[CLICK
HERE for the Full Blog Message with expanded discussions of these Insights]
Key Insight #1: Math is
cumulative—unfinished learning from prior years makes it harder for students to
master more advanced concepts.
Key Insight #2: Current
educational policies favoring grade-level instruction (i.e., teaching students
at their current grade placements) are hindering many students’ longer-term
success.
Key Insight #3: Balancing pre-grade level, on-grade level, and
post-grade level skills to each student’s needs can better support their long-term
success.
_ _ _ _ _ _ _ _ _ _
Summary
This Blog Series has focused on the instructional
dilemma that occurs when students transition from elementary to middle
school—or middle school to high school—and their academic skill levels are so
low that (a) they have no hope of learning or succeeding in the courses at the
next grade level, and (b) their skill gaps are so significant that the
different remedial options that most schools use will not close the gaps.
During the discussion, the four Options that
most middle or high schools use to address this dilemma were described—noting
their differential strengths and weaknesses, and how schools miss (or ignore)
the fact that these options will not address these students’ significant needs.
We then detailed a number “stark realities”
that we summarized in the following ways:
· If middle school students with
significant academic skill gaps “pass” their courses, but do not master the
“elementary” and “middle school” skills that they need, we have simply
passed the “problem” on to the high school “to solve.”
· Moreover, if these students “pass”
courses and “graduate” from their high schools without mastering the
academic and related skills needed to truly succeed at the “college and/or
career level,” the schools have not accomplished their educational mission and
a disservice has been done to the students.
From a multi-tiered perspective,
then, the goal is to complete (a) a data-based problem-solving process that
links the results of a root cause analysis to strategic or intensive services,
supports, strategies, and interventions; and (b) to consider a fifth
option where students are taught at their functional skill and mastery levels,
and where they receive the interventions and supports needed to learn, master,
and progress through the academic skills needed to ultimately be successful at
their true grade levels.
_ _ _ _ _
This current Part II presented information
and data specifically in the area of mathematics. It was noted that, in contrast with literacy,
math tends to be more finite (i.e., there are right and wrong answers), more
dependent on specific mathematical algorithms (e.g., formulae or clear problem-solving
steps), and more sequentially scaffolded—with certain skills laying the “foundation”
as prerequisite skills to a next set of skills.
In addition,
large-scale longitudinal data were presented demonstrating that students in
fourth and eighth grade, respectively, who are “off track” and “far off track”
relative to their grade-level mastery and proficiency in math, maintained their
low academic standings four years later.
Additional information
was presented demonstrating that the first four “catch-up” Options discussed in
this Blog Series are questionable at best relative assisting students who are
significantly behind in math in both middle and high school.
_ _ _ _ _
All of this
suggests that middle and high schools need to seriously consider Option 5 for
significantly skill deficient students. This
Option involves scheduling students into courses (or a double-blocked course)
in their academic area(s) of deficiency that target focus instruction at students’
functional, instructional skill levels (and not at their current grade
placement). These courses should take
students from their lowest points of skill mastery (regardless of level), and
move them flexibly through each grade level’s scope and sequence as quickly as
they can master and apply the material.
These courses
should be the students’ only course in the targeted academic area, and
the course instructors are responsible for making the content and materials
relevant to the grade level of the student, even as they are teaching
specific academic skills at the students’ current functional skill levels.
_ _ _ _ _ _ _ _ _ _
I hope that the research,
information, and ideas in this Blog Series have been useful, and I appreciate
your ongoing support in reading this Blog.
As always, if you have comments or questions, please contact me at your
convenience.
And please feel
free to take advantage of my standing offer for a free, one-hour conference
call consultation with you and your team at any time.
Best,
Howie
