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Deepen Mathematical Understanding Through Writing

Guest Post Written By: Gretchen of Always A Lesson

The assumption many students have about learning math is that there is minimal writing required in order to understand the concepts. When in actuality, writing is very much a part of the learning process. In fact, when done successfully, writing can deepen a student’s understanding of mathematical concepts.

Writing does not have to be a separate subject only taught in isolation. It can be taught at the same time as math because writing is a means by which to learn something rather than just a subject taught in school. It provides the brain additional think time to process concepts as the hand writes on paper. As a result, teaching these two subjects together only enhances the learning experience for students because they can strengthen their writing skills while computing and strengthen their math skills while writing.

Students tend to struggle in math due to a lack of time and effort to process the newly taught concepts, both of which can be eradicated by teachers implementing more writing activities into their lessons. Currently, in most math classes, students do not write for extensive periods of time or even often enough. Of course, students write numbers to solve math problems, but rarely do they write using words to express their thinking. This lack of writing in the learning process is a missed opportunity to help students gain proficiency in mathematical concepts.

Knowing that writing can enhance student skillsets in math, teachers need to build time for it into their math instruction. They can start by giving writing assignments in small increments, slowly adding in more writing time over subsequent weeks until students are writing and solving math problems in unison. It might feel awkward at first for students, but so do most new skills while you are acquiring them. Over time, writing and solving math problems in unison will become habit and feel quite natural for everyone.

There are a variety of ways in which teachers can weave writing in throughout their math block- before, during, and after learning experiences.

Gearing Up for Learning

A pre-learning activity helps students’ brains get into ‘learning mode’ before jumping into the heavy content of the lesson. Teachers should take advantage of this method by incorporating a small writing activity for students to complete at the start of the math lesson.  Warming up through writing about math can be completed in just a matter of minutes.

Students can…

• Review the lesson objective or topic and write their predictions for what they think they will learn, how they will learn it, why it is important, and so on
• Goal set by reviewing past learning goals, track current ones, set new goals, etc.

(This writing activity is low risk since it is opinion writing, meaning there is no right or wrong answer and the focus is not on the perfection of students’ writing skills, but on the substance in the writing.)

Taking in Learning

Now that students have warmed up their brains and are ready to dive into the heavier content of the lesson, teachers can incorporate more substantial writing activities into the math instruction to aid in student learning.

Students can…

• Take notes on math problem solving strategies, vocabulary, or algorithm procedures
• Make simple observations in writing about math problems completed in a model demonstration by the teacher prior to a class discussion
• Complete a ‘Stop and Jot’ on a sticky note to record a thought, question, comment, or response to a mathematical prompt before moving on in the lesson

These activities are more extensive than a pre-writing activity but are still brief enough to keep the lesson moving. This short writing opportunity creates a mental math break and enables students to comprehend content in smaller chunks so that the concepts can sink in before tackling more information. As a result, students are armed with a stronger knowledge base that increases their confidence to correctly complete math assignments now and in the future.

Demonstrating Learning

It is of utmost importance that students demonstrate their learning as soon as possible in order to solidify the newly learned knowledge. It is especially true in math, where much of the concepts are achieved through repetitive practice.

Instead of having students complete math problem after math problem, teachers can mix up the learning experience with writing activities.

Students can…

• Write the rationale for how they solved a math problem with a specific strategy
• Review a peer’s work for potential errors they made and reply with written clues to help them fix it
• Complete a ‘Graffiti Walk,’ where students rotate from table to table filled with work samples and write graffiti-style on the paper with their comments
• Use a writing prompt to reteach a mathematical procedure or concept to a peer pen-pal

(This could be completed in a journal format throughout the year for different concepts taught.)

• Prepare for an active class discussion by writing a reflection to gather their thoughts

Continuing Learning

Just because the math lesson stops when the bell rings, doesn’t mean the learning has to stop for students. Additional math-based writing opportunities can be included in the learning experience after class is over.

Students can…

• Complete daily reflections on what they learned that day, what they struggled with, strategies they are comfortable using to solve complex problems, etc.
• Write in their journals to a peer pen pal to reteach concepts in a variety of ways (similar to how a teacher will differentiate to teach the same concept multiple ways to meet student needs)
• Take a peer’s math work paper home and write a letter back to them including praise for the strengths in their work and suggestions for correcting errors

Students can hone their math skills through a variety of writing activities before, during and after their learning experiences. It is important that the writing activities are low stakes to encourage participation rather than perfection. When teachers avoid correcting writing abilities and focus on writing as a mode by which to process math concepts, students will begin to rely on using writing as a comprehension method. This increases student comfortability and confidence. Writing is simply an additional strategy they learn to use in efforts to gain a deeper understanding of mathematical concepts.

The Secret to Achieving Mastery in Math

Guest Post Written By: Gretchen of Always A Lesson

Students come to school to learn and it is the job of educators to ensure that happens when students are in their classroom. The goal in helping students learn is to achieve proficiency in the subject taught so that they have a firm foundation as they continue on in their journey in learning and life. For many educators though, they desire more than proficiency for their students and work hard to ensure that every student achieves mastery instead.

Skill Acquisition

Proficiency takes time and repetition in the short term where mastery takes time and repetition in the long term. It is the difference between knowing something today and knowing something every day. Although proficiency will ensure students are prepared for the next grade level, mastery ensures students take that knowledge base with them into their future.

Old Instructional Design

In order to achieve mastery for all students, teachers have had to ditch their past instructional habits; ones that had dismal results because students struggled in Math and had a lack of motivation to get better at it. The old method included this series of instruction:

• Teacher used direct instruction to deliver a math concept one time to all students
• Students repetitively practiced the concept independently in and out of class
• Teacher provided an assessment on the concept and recorded student scores in the grade book
• Teacher moved on to a new concept to repeat this same series of instruction all over again

It is no wonder that old method of instruction did little to motivate students- it was dry and boring. Students that were “good” at Math continued to be good at Math and those that were “not good” at Math continued to not be good at Math. Proficiency was barely reached, meaning mastery was nowhere in the picture.

New Instructional Design

To overcome the obstacle of low student performance and motivation in Math, teachers are now switching up their instructional method to better meet the needs of all students. The new method includes this series of instruction:

• Teacher provides pre-assessment to students to determine the degree to which they understand the soon-to-be taught concept
• Teacher uses the pre-assessment data to create a personalized lesson plan tailored to the knowledge level of their current students
• Teacher delivers a direct instruction mini lesson that includes modeling of a mathematical skill, followed by guided practice with students
• Students repetitively practice the mathematical concept independently while the teacher provides differentiated support as needed
  • Option A: Teacher conferences 1:1 with students on current concept
    • Tip– Be sure to keep a record for each student so that you can recall what skill you worked on previously, set goals, and make note of any pertinent details (ie. common mistakes)
  • Option B: Teacher uses small group instruction to reinforce old and new math concepts taught
    • Tip– Keep groups intimate, ideally 2-5 students, so that students receive targeted instruction on their current struggles or weakness.
    • Tip– Reference informal and formal data points to formulate student groupings based on similar struggles
    • Tip– Keep a record of who you met with, when you met, and what you worked on to help you plan future groups and recall pertinent details of those meetings
  • Option C: Teacher designs learning centers with review activities for repeated practice for all students, including an accountability assignment to inform the teacher of student performance
    • Tip– Create hands-on activities (or have math tools on hand) for tactile learners
    • Tip– Only put previously taught skill activities in centers so students need little direction from the teacher
    • Tip– Implement an accountability system that requires students to demonstrate their learning (ie. show their work, write a journal entry, fill out a survey, etc.)
  • Teacher provides post- assessment (similar to the pre-assessment formatting and questions) on the mathematical concept to showcase student growth
  • Teacher moves on to a new concept to repeat the same series of instruction all over again

This new instructional method is much more involved than the previous technique, allowing teachers to both formally and informally collect data points on student performance throughout a single lesson and then adjust their support in the moment as needed. The teacher is now more in tune with student skill levels and can create learning experiences to address any and all deficits.

Mastery in the Making

This new series of instruction has been extremely successful in not only overcoming the previous obstacles of student performance and motivation, but also in turning student proficiency into mastery. So, what is the secret?

For starters, it is clearly not dry and boring like the old method of instruction due to the numerous opportunities students have to practice mathematical skills in a variety of settings. Although students might be practicing the same skill repetitively, the novelty of the way in which they are practicing (small group, one-on-one, whole group, centers, etc.) is exciting and motivating. Therefore, students that were once “good” at Math got even better and students that were “not good” at Math got to experience many moments of “getting it.”

Secondly, educators know that differentiation ensures a multitude of learning needs are met during classroom instruction. But, this new teaching approach adds in one more important layer other than simply differentiating lesson plans. By moving beyond students practicing one mathematical concept in isolation before moving on to the next one, students are now practicing multiple previously learned skills simultaneously.

This new teaching approach is called ‘spiraling’ instruction. This means that teachers circle back (like a spiral) to old content while adding in new content to keep all skills fresh in students’ minds. Since students are getting multiple opportunities to achieve mastery, it increases their competency and confidence in Math.

In efforts for educators to recall the secret (and all of its instructional components), the reminder below can be helpful:

S-mall group instruction

P-roficiency then mastery

I-ndividualized instruction

R-eview of past skills
A-dditional practice of concepts

L-ong-term strategy for achievement

As with learning any new skill, practice is essential. With the spiraling instruction approach, students get plenty of practice throughout the school year on all of the mathematical skills required to progress to the next grade level and beyond. The thorough review and extended practice opportunities provided by this model result in a deep understanding of mathematical concepts for all students.

What tips can you add for how to spiral skills in the classroom?