TEACHING STRATEGIES FOR DIVERSE LEARNERS 2
Instructional Overview
For this assignment, I am using a class of twenty-five seventh grade students in a general
education mathematics classroom setting. This is a Title 1 school that uses a block schedule
system for core classes with rotating electives. Students in this setting typically test below
mastery in the majority of math concepts, especially in foundational skills. For this lesson, I will
be addressing standard 7.MG.2, “The student will solve problems and justify relationships of
similarity using proportional reasoning,” focusing specifically on D, “write proportions to
express the relationships between the lengths of corresponding sides of similar quadrilaterals and
triangles” (Mathematics | Virginia Department of Education, n.d.).
This standard focuses on proportional reasoning and writing proportions, to effectively
integrate these concepts into instruction for a diverse 7th-grade general education mathematics
classroom I would begin by checking for understanding of the prior knowledge needed for this
lesson and assess student readiness. I would use a simple pre-assessment to help understand
students' readiness levels regarding proportional reasoning, to help tailor instruction to meet the
diverse needs of the class. Before moving into proportional reasoning, students should show
background knowledge in geometry fundamentals, ratios, measurement concepts, and
multiplication and division skills (Yale National Initiative, n.d.).
During the lesson, I would also use visual aids such as diagrams, anchor charts,
geometric models, and manipulatives to help students visualize the concept of similarity and
proportional relationships. And I would incorporate interactive activities with manipulatives,
such as sorting shapes based on similarity, or having students mark and label corresponding sides
on manipulatives. It is also important to incorporate real-world examples and contexts to make
the concept of similarity and proportional reasoning more tangible and relevant to students' lives.
TEACHING STRATEGIES FOR DIVERSE LEARNERS 3
For instance, the class should discuss applications of similarity in architecture, map scaling, or
resizing images in graphic design, which can spark interest and facilitate understanding. This
also gives students the opportunity to incorporate culture, as we can use scale models of different
important buildings for reference.
Gifted Learners
In every classroom setting, there will be exceptional learners, including students
considered to be gifted learners who require a deeper level of engagement with the materials. For
this specific lesson, there are two strategies that I would incorporate to engage the gifted learners
using the strategies of tiered learning and allowing gifted students to work as a small group as
suggested in Six Strategies for Teaching Gifted Learners (Azzam, 2016). To accomplish this I
would group the gifted students in collaborative learning teams based on their levels of readiness
and interest (as determined in the pre-assessment). This will allow gifted learners to engage in
more challenging discussions regarding the geometrical concepts and provide opportunities for
cooperative learning and peer teaching.
Tiered learning allows for me to introduce more complex concepts and processes to the
gifted students, challenging them to mastery in the standard. I would develop tiered learning
pathways based on pre-assessment data and ongoing formative assessments of students'
understanding of similarity and proportional reasoning. For these gifted students, I would offer
tiered tasks that extend beyond the basic application of the standard "7.MG.2" and require deeper
analysis, synthesis, and evaluation of geometric concepts. This would include solving multi-step
problems involving similarity, proving geometric theorems, and exploring advanced geometric
constructions.
Struggling Learners
TEACHING STRATEGIES FOR DIVERSE LEARNERS 4
On the other end of the learning spectrum, are struggling learners. These could be
learners with diagnosed learning disabilities, or students who did not have mastery of
foundational mathematics concepts and are now behind in learning more advanced mathematical
concepts. That does not mean that these students are unable to learn these more advanced
mathematical concepts, instead it indicates that there needs to be differentiation in place to meet
the needs of these diverse learners. There are a few strategies recommended in the article 5
common techniques for helping struggling students (Osewalt, 2024) that would work well within
the lesson, graphic organization and multisensory instruction.
Graphic organizers are a great method for differentiation as they help students visualize
the concept while creating an attention-grabbing reference tool. I would use graphic organizers to
illustrate the relationships between geometric shapes, angles, and proportional sides. A graphic
organizer can show how corresponding sides of similar triangles are proportional and how this
relates to the concept of similarity. Scaffolded graphic organizers would provide partially
completed templates or fill-in-the-blank diagrams to guide struggling students through the
process of organizing their thoughts and connecting related concepts. These graphic organizers
can also be scaled up to challenge the gifted learners, and be used as a resource for English
Language learners.
Engaging students in multisensory instruction in mathematics can present a challenge for
many concepts. Fortunately, geometric concepts lend themselves to hands-on learning
experiences. I would use tactile materials like pattern blocks, tangrams, or geometric models to
allow students to physically manipulate shapes and explore the concept of similarity through
hands-on experience. I would supplement this with online manipulatives for students to model
and examine similar figures in a virtual 3-D space. In addition to the visual aids and
TEACHING STRATEGIES FOR DIVERSE LEARNERS 5
manipulatives I would also incorporate auditory elements, such as verbal explanations,
mnemonic devices, or rhythmic chants, to reinforce key concepts and provide additional auditory
cues for struggling learners.
English Language Learners
English Language Learners (ELL) students who have a first/native language other than
English or come from a home that has a language other than English, are a large portion of the
modern classroom environment as globalism continues to flourish. English Language Learners
make up a significant portion of this sample classroom environment, meaning that all lessons
must use strategies beneficial to engaging ELL students and ensuring their success. Fortunately,
many of the differentiation strategies for ELL students are also beneficial to gifted students and
struggling learners. For this reason I would use the strategies of visual aids and reasoning aloud.
These are strategies employed to help students unfamiliar with the complex mathematics
vocabulary (Noonoo, 2023).
Students Impacted by Trauma
Students impacted by trauma are an important portion of the classroom make up, and the
strategies used to create meaningful and impactful learning experiences can benefit the entire
class. These strategies also help create a safe and productive learning environment for students
affected by trauma and the students who are there to support them. The two strategies that fit best
with this lesson (and most math lessons) are giving supportive feedback to reduce negative
thinking and creating islands of competence (Minahan, 2019).
When working with trauma-impacted students in the context of the lesson on similarity
and proportional reasoning (standard "7.MG.2"), providing supportive feedback and creating
islands of competence are crucial differentiation strategies to foster a positive learning
TEACHING STRATEGIES FOR DIVERSE LEARNERS 6
environment and promote academic success. I would offer specific, constructive feedback that
focuses on students’ efforts, progress, and areas of improvement rather than focusing solely on
their academic performance, being sure to acknowledge and validate their efforts in attempting
challenging mathematical concepts. I would also encourage self-reflection and self-evaluation by
prompting students to identify their own strengths and areas for improvement. This will
empower them to set realistic goals and monitor their progress over time, fostering a sense of
agency and self-efficacy in their learning journey (Minahan, 2019).
Creating islands of competence refers to the practice of identifying and nurturing areas of
strength, skill, or competence within an individual, especially in situations where they may be
experiencing challenges or difficulties. For the context of this lesson on proportionality and
similar figures, it would look like identifying and capitalizing on the students’ areas of strength
within the context of similarity and proportional reasoning, as determined during the pre-
assessment. I would also offer a choice of learning and autonomy in the assignments that are part
of the learning process, giving students authority and responsibility over their learning and
providing the opportunity for students to use their interests to guide their learning(Minahan,
2019).
Conclusion
As seen throughout the paper, differentiation strategies can be beneficial to multiple
groups of learners. In a mathematics classroom it is vitally important that students are engaged
with the learning materials and understand the reasoning behind the mathematics. The strategies
listed here are simple for teachers to employ in both whole group and small group settings, and
as individual interventions as needed. Small group work helps reinforce concepts while
providing a space for academic discourse and peer review, an important part of fostering a safe
TEACHING STRATEGIES FOR DIVERSE LEARNERS 7
and encouraging learning environment. Providing visual aids helps ELL students, struggling
learners, and those with diverse learning preferences. Differentiation is an essential part of the
modern classroom, and every lesson benefits from some form of differentiated instructional
strategy.
TEACHING STRATEGIES FOR DIVERSE LEARNERS 8
References
Azzam, A. (2016, April 1). Six Strategies for challenging gifted Learners. ASCD.
https://www-ascd-org.eu1.proxy.openathens.net/el/articles/six-strategies-for-challenging-
gifted-learners
Mathematics | Virginia Department of Education. (n.d.). www.doe.virginia.gov/teaching-
learning-assessment/k-12-standards-instruction/mathematics
Minahan, J. (2019). Trauma-informed teaching strategies. Educational Leadership, 77(2),
30-35
Noonoo, S. (2023, February 16). 4 Strategies to help English learners master new math
skills. Edutopia. www.edutopia.org/article/4-strategies-to-help-english-learners-master-
new-math-skills
Osewalt, G. (2024, March 19). 5 common techniques for helping struggling students.
Understood. https://www.understood.org/en/articles/5-common-techniques-for-helping-
struggling-students
Yale National Initiative. (n.d.). 15.05.08: Equations in the Common Core: Algebraic
Reasoning and Problem Solving.
https://teachers.yale.edu/curriculum/viewer/initiative_15.05.08_u
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