As math teachers, we spend much of our time planning for students who need extra time or support to understand mathematics at our grade level. We also worry about how we might create appropriate challenge for students who have a strong foundation in math and are ready to move ahead before their classmates are ready. The last thing we want is for our most able mathematics students to get bored and disengage. Enrichment seems like a good option, but how do we do that?
Why? Goals
Enrichment activies are meant to allow students to
engage in rich tasks and activities at grade level
stay with their peers
replace foundational math tasks that other students require to build understanding
reinforce mathematical thinking skills so that students are even more able to engage in grade-level math
When? Timing
There are at least two opportunities for enrichment within your instructional sequence.
When we pause to help students review and build readiness for grade-level instruction. This might be in the form of a concept review, reteach, or responsive station.
Enrichment tasks can be an option for students who do not need to review or practice foundational skills.
Enrichment tasks that are loosely based on the same concepts as are in the review will help students be even more ready for grade-level instruction.
When we are teaching grade-level concepts and the majority of students require more time to complete tasks.
Enrichment tasks can be an option for students who are done work earlier than their peers.
Enrichment tasks that are loosely based on the grade-level concept, but allow for creative thinking and application can allow students to see mathematics in a creative and contextual way.
What? Characteristics
Enrichment tasks take on all different forms. Some common characteristics might be:
Engaging
Hands-on
Applied to the Real World
Creative
Games
Puzzles
Math Outside of Curriculum
Connecting Math Concepts
Social Justice topics
You can access hundreds of curated resources in this Enrichment Task Google Folder. Feel free to share, download, and use these resources.
Who? Target Students
All students might be able to engage in Enrichment tasks at some point in the year. Different students have different strengths. Enrichment is not exclusive to gifted students.
How? Classroom Structures
A station or enrichment corner are relatively simple to set up. One thing to consider is what tasks to have available at what time. A suggestion is that the tasks in the enrichment station should be loosely related to the math concept being experienced by the rest of the class. This ensures that the students doing enrichment tasks are going to be even more able to complete grade-level math tasks. When enrichment tasks are completely unrelated to the math students will experience next, we are inadvertently creating a time gap in student learning and may actually contribute to lower achievement.
How often have we been in a conversation with a colleague about trying to meet the needs of all of our students, and we hear the dreaded phrase “well, just differentiate”… this blanket statement can bring about visions of creating 18 different lesson plans for our 18 students. This is not sustainable, so what is differentiation REALLY? How do we meet the needs of diverse learners and keep our sanity?
Workshops focussing on differentiation are, ironically, often not differentiated. It is important that all professional learning, including those experiences based on the topic of differentiation, attempt to have teachers experience differentiated learning as well as reinforce the foundations of how and why we differentiate content, process, product and environment for students.
Planning for Differentiation
It is important to understand not only specific strategies but to also know why we might differentiate. What information do we need as teachers in order to plan appropriately for our individual students as well as our whole class experiences? We need to know a combination of Learning Styles, Multiple Intelligences, content readiness, and student interests in order to Plan for Differentiation.
Something that is often an ‘aha’ for adults is to consider whether they are “Think to Talk or Talk to Think” learners. If someone is a think-to-talker and is forced to jump into group work without first having the chance to get their thoughts in order, they may have a feeling of being unsafe expressing their ideas. If a talk-to-thinker is forced to read quietly before they are allowed to talk, they may find that their minds wander and are unable to focus. This same sense of safety is true for student learners as well.
One of the foundational researchers in the area of differentiation is Carol Tomlinson, who describes differentiation as
Being curious about our students,
Having relationships between teachers and students; and
Providing a variety of learning experiences to learners
Differentiating Content
Why:
Differentiating content allows you to address gaps in understanding to build readiness. We know in literacy that activating prior knowledge is essential for students to make connections to new learning. This is true in other subjects as well. Assessing prior knowledge allows gaps to be addressed before new concepts are introduced. Differentiating content allows students to ACCESS information and learning.
What:
Your curriculum drives the knowledge, concepts, skills, and understandings a student needs to know and use. While the curricular outcome cannot change for individual students, the delivery format for content such as video, readings, audio, reading level can be differentiated. Content can also be chunked, shared through visual graphic organizers, or addressed through jigsaws to reduce the volume of information each individual needs to interact with. Themes can be based on personal interest to increase interest and understanding if a specific topic is not required by the curriculum.
How:
Use pre-assessment to determine where students need to begin, then match students with appropriate activities. Pre-assessments may include:
Student/teacher discussion,
Begin a KWL chart – what we know/want to know/learned,
Journal – what you already know about,
Brain dump – list all of the things you know about a topic, cluster with other class members, and
Snowball.
Use texts or novels at more than one reading level.
Present information through both whole-to-part and part-to-whole.
Use a variety of reading-buddy arrangements to support and challenge students when working with different texts.
Re-teach students pre-skills or provide enrichment for students who already demonstrate an understanding of pre-skills.
Use texts, video or different media to convey information.
Use Bloom’s taxonomy or Webb’s depth of knowledge to encourage thinking about content at several levels.
Differentiation Process
Why:
Differentiating process is about how students make sense of new learning. What is happening in each individual brain is based on their learning preferences, multiple intelligences, and background. Learners need time to take in, reflect on and make sense of new learning before moving on. Processes help students monitor their comprehension and determine what they do and do not understand. Learning processes also allow teachers to formatively assess student progress and provide feedback in real time.
What:
There are many different words used to describe learning processes – instructional strategies, discursive strategies, comprehension strategies… all of these are ways that learners interact with and make sense of new learning. Providing more or less structured support for learning, planning for a variety of instructional strategies based on the variety of learning styles in a classroom during a unit of study, and providing opportunities for self-reflection and self-assessment, and providing individual, pair/small group and whole group learning experiences are some key ideas for differentiation process.
How:
Assess learning styles, multiple intelligences, learning preferences, etc. to understand individual learning profiles as well as your class profile.
Use tiered activities that allow all students to work on the same outcome but with different levels of support.
Provide different learning experiences based on interests – i.e. when exploring mixtures and solutions, some students might choose to learn concepts through cooking, while others may learn concepts through art.
When planning a unit of study, ensure that concepts are interacted with using a variety of modes. For example, in mathematics, a planning form for math could be based on the idea of multiple representations of mathematical ideas:
Use a variety of comprehension strategy tactics.
Provide choice for students for how they are going to take notes, summarize information, make connections.
Literature Circles(which also support content and product differentiation).
Different classroom structures, such as stations/centers, choice boards, flexible grouping all allow for different processes to be occurring simultaneously.
Differentiating Product
Why:
Differentiating product allows for student choice and allows learners to use their strengths to represent their understanding. Product choices all align to curricular outcomes, so learning is not compromised. Student voice and choice increase learner engagement. Products are the way that students represent their thinking about a curricular outcome. Differentiating the type of product being created allows you to see what they know about the curricular topic rather than the skill they needed to package that representation.
What:
Product differentiation is often cited as the most common form of differentiation and is often in the form of choices. You as the teacher may provide those choices and students pick from a variety of formats, you may have students propose their own designs or a combination of the two. How much responsibility and autonomy you provide for your students will depend on factors such as student understanding of their own strengths, age and time. When providing choice, it is important to co-construct clear criteria for success so that all products, regardless of form, are all being assessed on curricular outcomes rather than the form of a product. A rule of thumb is that the same checklist/rubric/assessment tool should be able to be used for all products on the same outcome, whether they are a paper, video, play, board game, etc.
How:
Allow students to help design product choices.
Co-construct assessment criteria.
Allow for varied working arrangements – individual, pair, group
Provide for or encourage students accessing a variety of resources.
Use a common assessment tool (checklist, rubric, etc.).
Conclusion:
When teachers plan by connecting content, process, product and learning product with student readiness, interests and learning profiles, students are more engaged and are able to understand ideas with a higher level of complexity.
Comprehension strategies are ways in which we make meaning of the information we take in through text, media, and sound. Often considered the domain of the English Language Arts teacher, we now realize that it is important that teachers across subject areas and grades encourage meaning making and use tactics that cause learners to use strategies that they may or may not be fluent in.
Depending on which researcher you follow, you may categorize comprehension strategies into 6, 7, or even 13 different strategies. Following the framework of Ellin Keene (1997) in her book Mosaic of Thought: Teaching Comprehension in a Readers Workshop, this post identifies seven strategies that help learners make meaning of complex information. A detailed comprehension strategies summary describes the actions of readers, writers, mathematicians, and researchers.
While categorizing strategies and tactics is helpful, we need to keep in mind that the comprehension strategies are all interconnected. Visualization is grounded on activating and connecting knowledge. Determining importance and summarizing are closely related. Monitoring comprehension often creates self-questions. Each person has different comprehension strategies that their mind tends to use. Our challenge as teachers is to create a pause and opportunity for students to try stretching to new mental pathways.
Activating and Connecting Prior Knowledge
This comprehension strategy involves students connecting their learning to past experiences, events in the world, and to other learning they may have in and out of school. We simply can’t understand new information that we hear, read or view without thinking about what we already know. It is important that teachers teach learners to:
Relate to prior experience.
Make connections between text, media, and personal observation.
Connect the new to the known – use what learners know to understand new information.
When students are using this comprehension strategy, you may hear them say…
This reminds me of…
I noticed…
It made me think of…
I never knew…
That changed my mind…
This is different from…
Some tactics that teachers might use to promote activating and connecting prior knowledge include:
This comprehension strategy involves students recognizing and acting on their own confusion, and their self-questioning to determine understanding. We monitor our comprehension and keep track of our thinking in a number of ways. We notice when text makes sense and when it doesn’t. We ask questions, infer, activate background knowledge, and make connections, all in the effort to promote understanding. It is important that teachers teach learners to:
Become aware of their thinking as they read.
Notice when meaning breaks down and their mind wanders.
Employ ‘fix up’ strategies – reread for clarification, read ahead to construct meaning, use context to break down unfamiliar words, skip difficult parts and continue to see if meaning becomes clear, check and recheck answers and thinking, and examine the evidence.
When students are using this comprehension strategy, you may hear them say…
I think…
I understand…
This doesn’t make sense…
Oh, now I get it…
A part I had trouble with…
Some tactics that teachers might use to promote monitoring comprehension include:
This strategy involves students actively wondering about topics and questioning facts and information. Questioning is the strategy that propels learners on and is at the heart of inquiry-based learning. Humans are driven to make sense of the world, and questions open the doors to understanding. It is important that teachers teach learners to:
Wonder about the content, concepts, outcomes, and genre of text.
Question the author.
Read to discover answers and gain information.
When students use this comprehension strategy, you may hear them say…
I wonder…
I’m curious…
My big question is…
Why…
Do you know anything about…
Some tactics that teachers might use to promote questioning include:
This comprehension strategy involves students predicting, hypothesizing, interpreting, and making conclusions. Inferential thinking allows learners to grasp the deeper essence of text and information. Readers infer by taking their background knowledge and merge it with clues int he text to draw a conclusion or arrive at a big idea that is not explicitly stated in the text. It is important that teachers teach learners to:
Use context clues to figure out meaning of unfamiliar words.
Draw conclusions from evidence.
Predict outcomes, events and observations.
When students use this comprehension strategy, you may hear them say…
I’m thinking…
It seems to me…
I’m guessing that…
I predict…
Probably…
Some tactics that teachers might use to promote inferring include:
This comprehension strategy involves students evaluating information, making judgments about information, and identifying key ideas and concepts. We read nonfiction to learn, understand, and remember information. It is important that teachers teach learners to:
Target key information.
Choose what to remember.
Construct big ideas from smaller ideas.
When students use this comprehension strategy, you may hear them say…
This is really important…
The most important ideas here are…
So far, I have learned that…
I think this part means…
Some tactics that teachers might use to promote determining importance include:
This comprehension strategy involves students making mental pictures and/or mind maps of ideas and how they interconnect. Visualization builds complex connections and involves more than just how something looks. It extends to other senses such as smell, touch, sound, and taste. It is important that teachers teach learners to:
Gain information from the images they construct and view.
Create mental images drawn from background knowledge and observations.
When students use this comprehension strategy, you may hear them say…
I am getting a picture…
I can see (smell, hear, taste)…
I have a picture in my head…
Some tactics that teachers might use to promote visualization include:
This comprehension strategy involves students recalling, retelling, creating new meaning, and remembering information. Synthesizing information allows us to see the bigger picture as we read or observe. Thoughtful readers merge their thinking with information to come to a more complete understanding. It is important that teachers teach learners to:
Add to their knowledge base.
Paraphrase information
Move from facts to ideas.
Summarizing and synthesizing are often used as synonyms. While they are related, they are different strategies that readers use. Sarah Eaton, a professor at the University of Calgary (2010, Summarizing vs Synthesizing), identifies these differences:
Summarizing
Synthesizing
A basic reading technique.
An advanced reading technique.
Pulls together information in order to highlight the important points.
Pulls together information not only to highlight the important points, but also to draw your own conclusions.
Re-iterates the information.
Combines and contrasts information from different sources.
Shows what the original authors wrote.
Not only reflects your knowledge about what the original authors wrote, but also creates something new out of two or more pieces of writing.
Addresses one set of information (e.g. article, chapter, document) at a time. Each source remains distinct.
Combines parts and elements from a variety of sources into one unified entity.
Presents a cursory overview.
Focuses on both main ideas and details.
Demonstrates an understanding of the overall meaning.
Achieves new insight.
Summarizing is taking the details of information apart while synthesizing is putting those details back together into a new and unique whole.
When students use this comprehension strategy, you may hear them say…
I never knew… now I know…
I think the big idea is…
I have learned that…
Now I understand that…
Some tactics that teachers might use to promote summarizing and synthesizing include:
When do we explicitly use Comprehension Strategy Tactics?
If the information that we are having students interact with is complex, it is important to use instructional methods that help them make meaning. As well, if we notice that students are struggling with a specific skill or content area, we can view comprehension strategy instruction a possible solution to those learning barriers. Teaching with comprehension in mind will lead to increased cognitive engagement and deeper meaning-making.
Eaton, S. E. (2010, September 26). Reading Strategy: The difference between summarizing and synthesizing. Retrieved from http://www.drsaraheaton.wordpress.com
Johanson, T., & Broughton, D. (2014). Exploring Comprehension in Physics. Saskatoon: McDowell Foundation.
Keene, E., & Zimmermann, S. (1997). Mosaic of Thought: Teaching Comprehension in a Readers Workshop. Portsmouth: Heinemann.
Public Education & Business Coalition. (n.d.). Thinking Strategies for Learners: A guide to PEBC’s professional development in reading, writing, mathematics and information literacy. Retrieved December 15, 2018, from Public Education & Business Coalition: https://www.pebc.org/wp-content/uploads/publications/thinking-strategies.pdf