Personalized Learning and Mathematics Teaching and Learning
September 2018
Personalized learning is one of many
instructional approaches to support mathematics teaching and learning. However,
a consensus on the definition of personalized learning is lacking, which leaves
a range of ideas on what it might entail. These may include (a) customization, (b) student groupings, and (c)
flexibility of instruction. Customization focuses on tailoring experiences and
instruction for students’ needs, interests, goals, and backgrounds. This
suggests that personalized learning should have some humanizing aspects focused
on knowing and understanding who students are as people and as learners of
mathematics. Discussions on student groupings in personalized learning range
from one-to-one (one-on-one) to small groups to whole-class experiences. Too
often one-to-one and whole-class approaches are positioned in contrast; in fact,
they can be complementary for deepening students’ understanding of mathematics
and for supporting them to develop a positive personal relationship with
mathematics. Flexible instruction includes not only pacing of instruction but
also time and space for students to engage with mathematics.
Personalized
learning is often part of an instructional approach that supports the needs of individual
learners. Many perspectives on
personalized learning have focused primarily on improving test scores and
achievement while ignoring the humanizing and social aspects of mathematics
teaching and learning. For example, I have been exposed to several
approaches to personalized learning that focused on tailoring mathematics tasks
and problems to learners to find solutions with little emphasis on how they make sense of mathematics,
how they use their mathematical understanding to find solutions, and why their
solutions do or do not make sense. Personalized learning can be a space in
which learners give voice to the ways they think mathematically, represent and
discuss their mathematical ideas, and use mathematics to make sense of their
worlds. Personalized learning can help learners see themselves as doers
of mathematics by providing supports for developing understanding and perseverance,
as well as for engaging in collaborations with peers to unpack mathematical
thinking.
Imagine personalized learning as each and
every student being provided with a personalized teacher of mathematics who
understands his or her needs, knows his or her interests and background, and is
highly knowledgeable about mathematics teaching and learning. Imagine students
having broad access to their personalized teacher to ask questions and that their
personalized teacher is able to extend their mathematical thinking. While I
recognize that one-on-one instruction is unrealistic, I still grapple with whether
this condition of having a personalized teacher for personalized learning would
be enough for students to be productive learners of mathematics in a democratic
society. I grapple with this because I find value in students being connected
to other students who are diverse in their thinking about mathematics, have
diverse backgrounds to bring different perspectives about mathematics
representations and ideas, have varying worldviews, and are co-learners for
clarifying and critiquing one another’s mathematical ideas. My grappling makes
me think about ways that personalized learning is connected to ambitious
mathematics teaching and about how personalized learning could support
individual learners while creating spaces for individuals to engage other
learners.
I often draw on
the eight Mathematics Teaching Practices in NCTM’s Principles to Actions:
Ensuring Mathematical Success for All (NCTM, 2014) as a framework for unpacking mathematics
teaching and learning. Below are descriptions of the teaching practices with
questions to ponder that are related to personalized learning for mathematics.
1. Establish mathematics goals to focus
learning.
- How does personalized learning support
learning progressions that build up students’ mathematical understanding,
increase student confidence, and support mathematical identity?
- How does personalized learning ensure that
each and every student has the opportunity to learn rigorous mathematics
content and develop mathematical processes and practices?
2.
Implement tasks that promote
reasoning and problem solving.
- How
does personalized learning support tasks that require reasoning, problem solving,
and mathematizing our world through mathematical modeling?
- How
does personalized learning support culturally relevant mathematics tasks?
3.
Use and connect mathematical
representations.
- How
does personalized learning support the use of multiple representations so that
students can draw on multiple resources and funds of knowledge?
- How
does personalized learning ensure that students develop connections among
multiple representations to deepen their understanding of mathematical concepts
and procedures?
4.
Facilitate meaningful mathematical
discourse.
- How
does personalized learning use discourse to elicit students’ ideas and create
space for students to interact with peers?
- How
does personalized learning allow students to develop language to express
mathematical ideas and how does it position each learner with mathematical
authority and competence?
5.
Pose purposeful questions.
- How
does personalized learning pose purposeful questions to understand students’
mathematical thinking?
- How
does personalized learning support purposeful questions to deepen students’
mathematical understanding?
6.
Build procedural fluency from
conceptual understanding.
- How
does personalized learning connect conceptual understanding to procedural
fluency to provide students with a wide range of options for entering a task
and building mathematical meaning?
- How
does personalized learning routinely connect conceptual understanding and
procedural fluency to deepen learning and reduce mathematical anxiety?
7.
Support productive struggle in
learning mathematics.
- How
does personalized learning allow time for students to wrestle with mathematical
ideas in ways that support perseverance and sense making?
- How
does personalized learning offer enough support and scaffolding (without over-scaffolding)
to facilitate students’ progress on challenging work?
8.
Elicit and use evidence of student
thinking.
- How
does personalized learning elicit students’ thinking and make use of it to
support learning?
- How
does personalized learning support a culture in which mistakes and errors are
viewed as important reasoning opportunities?
I encourage you to use the questions above
to begin discussions on personalized learning in mathematics teaching and
learning. I am interested in learning about the promises and challenges of
personalized learning. Please share your successes and challenges on
MyNCTM.org
Robert Q.
Berry, III
NCTM President
National Council of Teachers of
Mathematics (NCTM). Principles to
Actions: Ensuring Mathematical Success for All. Reston, VA: NCTM, 2014.