Research References
Barbieri, C., & Booth, J. L. (2016). Support for struggling students in algebra:
Contributions of incorrect worked
examples.
Learning and Individual Differences, 48(1), 36–44.
https://eric.ed.gov/?id=ED566951
From the ERIC abstract: “Middle school algebra students (N = 125) randomly
assigned within classroom to a Problem-solving control group, a
Correct worked examples control group, or an Incorrect worked examples group,
completed an experimental classroom study
to assess the differential effects of incorrect examples versus the two control
groups on students’ algebra learning,
competence expectancy, and sense of belonging to math class. The study also explored
whether prior knowledge impacted
the effectiveness of the intervention. A greater sense of belonging and competence
expectancy predicted greater learning
overall. Students’ sense of belonging to math and competence expectancies were high
at the start of the study and did
not increase as a result of the intervention. A significant interaction between
prior knowledge and incorrect worked
examples on post-test scores revealed that students with low prior knowledge who
struggle with learning
math benefit most from reflecting on highlighted errors within an incorrect worked
examples intervention. The unique contributions of these findings as well as
educational
implications are discussed.”
Bell, C. V. (2013). Uptake as a mechanism to promote student learning.
International Journal of
Education in Mathematics, Science and Technology, 1(4), 217–229.
https://eric.ed.gov/?id=EJ1057556
From the ERIC abstract: “This study is a descriptive examination of uptake
that occurred
during classroom discourse in 33 Algebra I classrooms in nine U.S. states. Uptake
refers
to the act of taking up mathematical comments, questions, and constructions as
objects of
discourse. Uptake is important because it can be used for scaffolding authentic
opportunities to learn and promoting productive dispositions toward learning. Data
used
in this study were taken from video-recorded and transcribed observations of 63
class
sessions—30 participating teachers were observed twice and 3 were observed only
once.
Coding of uptake data resulted in 5 categories of types of utterances being taken up
and
16 categories of how the utterance was used in the episode of uptake. Analysis
across all
categories indicates that teachers most frequently provided mathematical
explanations
and reasoning, even when asking for students’ reasoning and explanations, which
limited
students' opportunities to express mathematical reasoning. Episodes of uptake
resulting in
more dialogic interaction did occur, but were relatively rare. Findings of this
study have
potential to help teachers and teacher educators become more aware of using uptake
to
strategically foster more authentic, student-centered discourse environments and
increase
students' opportunities to learn.”
Bissell, A. N. (2012). Architecture and impact of an open, online, remixable, and
multimediarich
Algebra 1 course.
Journal of Asynchronous Learning Networks, 16(5), 49–59.
https://eric.ed.gov/?id=EJ1000090
From the ERIC abstract: “Less than half of the students in the United States
graduate
from high school and are ready to take college-level math courses. Many years and
varieties of remedial math programs have failed to dramatically improve outcomes,
especially at scale. The question we face is whether technology in general, and open
educational resources in particular, might offer some solutions for improving math
scores
across the nation. Herein, we describe the work of the Monterey Institute for
Technology
and Education, and specifically the design and early evidence of impact of their
multimedia Algebra and Developmental Math resources. We believe that the structure
and function of these open educational resources can effectively meet the diverse
needs
of the nation’s math teachers and learners, perhaps paving the way to more
personalized
teaching and learning practices.”
Gilbert, J. E., Arbuthnot, K., Hood, S., Grant, M. M., West, M., McMillian, Y., et
al. (2008).
Teaching algebra using culturally relevant virtual instructors.
The International Journal
of Virtual Reality, 7(1), 21–30. Retrieved from
https://www.researchgate.net/publication/220222148
From the abstract: “When culture is integrated into the mathematics
classroom, it
improves students’ academic achievement [3], helps move classrooms towards an
equitable learning environment [30] [31], helps students have positive beliefs about
mathematics [23], and integrates mathematics with other disciplines [56], [58].
Moreover,
if you observe today’s kids, the use of video games in their daily and/or weekly
routines
is significant. Lastly, the predominant genre among African-American youth is
hiphop/
rap. These facts led to the African-American Distributed Multiple Learning Styles
System (AADMLSS pronounced ‘adam less’) City Stroll, an adaptive, electronic,
speechenabled
algebra learning system that uses culture to influence learning in the form of an
animated, music-led interface.”
Hodgson, T. R., Cunningham, A., McGee, D., Kinne, L. J., & Murphy, T. J. (2017).
Assessing
behavioral engagement in flipped and non-flipped mathematics classrooms: Teacher
abilities and other potential factors.
International Journal of Education in Mathematics,
Science and Technology, 5(4), 248–261.
https://eric.ed.gov/?id=EJ1151444
From the ERIC abstract: “There is a growing evidence that flipped classrooms
are
associated with increased levels of student engagement, as compared to engagement in
‘traditional’ settings. Much of this research, however, occurs in post-secondary
classrooms and is based upon self-reported engagement data. This study seeks to
extend
existing flipped classroom research by assessing behavioral engagement in flipped
and
non-flipped settings using observational instruments in three precollege settings.
Contrary
to widely-reported results, this study found an increase in engagement in only one
of the
three observed settings. Analyses of the classroom contexts and teachers’ actions in
the
three settings suggests that student engagement is not solely a function of
instructional
strategy (flipped versus non-flipped), but is also affected by student
characteristics and
teachers’ skill and expectations.”
McCaffrey, T., & Matthews, P. (2017). An emoji is worth a thousand variables.
Mathematics
Teacher, 111(2), 96–102.
https://www.researchgate.net/publication/319254337
From the abstract: “In this article, the authors discuss the potential of the
icon-based
mathematical games, emoji math and mobile math, to promote student engagement with
and understanding of algebra. They describe how these games serve as accessible
entry
points for algebraic thinking and that, in contrast to traditional symbolic algebra,
the
use of these icon-based games appears to be more meaningful to many students.
Because the games correspond to symbolic algebra, the authors suggest that they may
serve as powerful bridging functions for fostering students’ understanding of
symbolic
algebra in typical classrooms.”
Norton, A., & Rutledge, Z. (2006). Measuring task posing cycles: Mathematical letter
writing
between algebra students and preservice teachers.
Mathematics Educator, 19(1), 32–45.
https://eric.ed.gov/?id=EJ882223
From the ERIC abstract: “In a secondary school mathematics teaching methods
course, a
research team engaged 22 preservice secondary teachers (PSTs) in designing and
posing
tasks to algebra students through weekly letter writing. The goal of the tasks was
for
PSTs to elicit responses that would indicate student engagement in the mathematical
processes described by NCTM (2000) and Bloom’s taxonomy (Bloom, Englehart, Furst,
Hill, & Krathwohl, 1956), as well as student engagement in the highest levels of
cognitive activity described by Stein, Smith, Henningsen, and Silver (2000). This
paper
describes our efforts to design reliable measures that assess student engagement in
those
processes as a product of the evolving relationship within letter-writing pairs.
Results
indicate that some processes are easier to elicit and assess than others, but that
the letterwriting
pairs demonstrated significant growth in terms of elicited processes. Although it
is impossible to disentangle student factors from teacher factors that contributed
to that
growth, we find value in the authenticity of assessing PSTs’ tasks in terms of
student
engagement rather than student-independent task analysis.”
Robertson, W. H., Meyer, R. D., & Wilkerson, T. L. (2012). The mathematics of
skateboarding:
A relevant application of the 5Es of constructivism.
Journal of Education and Learning,
1(2), 32–36.
https://eric.ed.gov/?id=EJ1081355
From the ERIC abstract: “Getting high school students to enjoy mathematics
and
to
connect concepts to their daily lives is a challenge for many educators. The
Mathematics
of Skateboarding demonstrated innovative and creative ways to engage students in
content and skills mapped to state requirements for high school students in Algebra
and
Geometry.”
Star, J. R., Foegen, A., Larson, M. R., McCallum, W. G., Porath, J., & Zbiek, R. M.
(2015).
Teaching strategies for improving algebra knowledge in middle and high school
students.(NCEE 2015–4010). Washington, DC: National Center for Education
Evaluation and
Regional Assistance, Institute of Education Sciences, U.S. Department of Education.
https://eric.ed.gov/?id=ED555576
From the ERIC abstract: “Mastering algebra is important for future math and
postsecondary success. Educators will find practical recommendations for how to
improve algebra instruction in the What Works Clearinghouse (WWC) practice guide,
‘Teaching Strategies for Improving Algebra Knowledge in Middle and High School
Students’. The methods and examples included in the guide focus on helping students
analyze solved problems, recognize structure, and utilize alternative approaches to
solving algebra problems. Each recommendation includes the level of supporting
research evidence behind it, examples to use in class, and solutions to potential
implementation roadblocks. Teachers can implement these strategies in conjunction
with
existing standards or curricula. In addition, these strategies can be utilized for
all students
learning algebra in grades 6–12 and in diverse contexts, including during both
formative
and summative assessment. Administrators and professional development providers can
use the guide to implement evidence-based instruction and align instruction with
state
standards or to prompt teacher discussion in professional learning communities.”
Additional Organizations to Consult
The Algebra Project —
https://algebra.org/wp/
From the website: “The Algebra Project’s founder and participants have worked
in
classrooms for two decades to develop classroom teaching methods, teacher
professional
development, and community development that will enable students to succeed in a
typical Algebra I course in late middle school or early high school.
Originally, the project targeted classrooms with large proportions of African
American
students. Recently, the project has been invited to work in sites with large
Latino/a
populations with varying heritage (e.g. Yuma, AZ; Boston; Chicago; Miami), and has
been contacted by sites with other underserved populations.
Originally, the project targeted middle schools, addressing the transition from
arithmetic
to algebraic thinking. In 1995, founder Robert Moses began addressing high school
mathematics, working at Lanier High School, the lowest performing high school in
Jackson, MS, and with interested university mathematicians, resulting in NSF grants
in
2002 and 2006 to develop instructional materials for high school beginning algebra.
The Algebra Project received a four-year NSF grant in 1997 for teacher professional
development and site community development. Recently, the project’s youth initiative
(the Young People’s Project) received an NSF grant to develop college and high
school
mathematics literacy workers who lead out-of-school sessions for younger students
upon
invitation from community based organizations.”
REL Southwest note: Two relevant case studies from The Algebra Project are
available
in
ERIC:
Gilbert, J. E., Eugene, W., Swanier, C., Arbuthnot, K., Hood, S., Grant, M. M., et
al.
(2008). Culturally relevant design practices: A case study for designing
interactive algebra lessons for urban youth.
Journal of Educational Technology,
5(3), 54–60.
https://eric.ed.gov/?id=EJ1097826
Grant, M. R., Crompton, H., & Ford, D. J. (2015). Black male students and The
Algebra
Project: Mathematics identity as participation.
Journal of Urban Mathematics
Education, 8(2), 87–118.
https://eric.ed.gov/?id=EJ1086176
The Nellie Mae Education Foundation —
https://www.nmefoundation.org
From the website: “The Nellie Mae Education Foundation has been committed to
reshaping the high school learning experience by working with districts, schools and
organizations to implement the principles of student-centered learning—learning that
is personalized, engaging, competency-based and happens anytime, anywhere."
What Works Clearinghouse (WWC) What Works in Math —
https://ies.ed.gov/ncee/wwc/Math/
From the website: “What Works in Math?
There’s no single answer to that broad question. Instead, what works varies by
grade,
subject, and even delivery model.
WWC products allow educators to better understand what works in different contexts.
WWC intervention reports show which tools increase mathematics achievement by
grade, while WWC practice guides show effective practices for topics such as
fractions.
Search our publications
here."