Many parents ask me why their child's school no longer requires math textbooks.
Without math textbooks, parents are concerned that they don't have a guide to follow along with, and any parent wants to help their kid learn by first knowing what they're learning.
Without a textbook, parents are concerned that they don't know what their child is learning. Some schools use formative assessment systems and communicate to parents on a mobile app or over the internet. Some schools change their math textbooks or programs every few years.
The big question is always "should we be concerned" because parents have the right to know what their kids are learning. Knowing what students are learning requires a curriculum.
In this post, I'll discuss the importance of math curriculum. Textbooks are excellent tools to foster home and school communication, but the presence or absence of a textbook tells you nothing about a school's math curriculum.
If you're worried that your kids don't have a math textbook, you should be a hundred times more worried if their school lacks a curriculum.
Let’s start with something that most of us already know about - but before we start, let’s quickly answer the question, “what is a curriculum?”
A curriculum is an organized list of topics that guide the process of teaching and learning about a subject. A curriculum is useful when it includes broad topics that can be translated into goals and objectives to guide assessment.
Curricula (the plural of curriculum) are also called “programs,” “frameworks,” or “courses of study,” because they are carefully planned and arranged.
Just about everything that you could learn or teach has a curriculum. Using a curriculum becomes critically important when we need to teach something to someone else.
Let’s say you had to teach someone how to clean your house. Whether you mean to or not, you’d probably use a house-cleaning curriculum. What would your clean-house curriculum look like?
To start any house-cleaning curriculum, it would be helpful to start with inclusive things that are in all rooms like floors, surfaces, and walls. Another way to start would be to list areas of the house like the kitchen, stairs, bathrooms, and bedrooms. Notice how floors, surfaces, and walls are really inclusive because most rooms contain these features. So, it would be better to start our house-cleaning curriculum with broad and inclusive topics.
In any math curriculum, it's also helpful to start with broad and relevant areas. In math, broad and relevant topics are things like counting, proportional thinking, wholes / parts, and quantity and denomination - areas that cut across all subjects like pre-algebra, geometry, or calculus. Think of counting and proportional thinking like floors and surfaces while pre-algebra and calculus are like the living room or kitchen.
Whether it’s house cleaning or math, helping someone to learn a topic requires an organized and relevant set of goals, like “improve the cleanliness of the kitchen,” or “reduce the clutter in the living room.”
To help meet goals, curricula (the plural of curriculum) include objectives, which are like goals but provide specific guidance with clearer verbs than those contained in goals.
The verb “to improve” the cleanliness of the kitchen might be unclear because two people may have different ideas about what it means to have a clean kitchen.
What if we instead used a highly specific objective like “wipe down the stove with spray cleaner each morning,” then we’ve got two great things: (a) a clear guide to action and (b) a way to communicate with others and gain broad agreement about what constitutes the basic standards for a clean kitchen.
Let’s say you found a book called, “The Ultimate Guide to House Cleaning,” and in the table of contents was a list of different areas of a home. When you turn to the chapter on kitchens, you notice that the goals are to maintain a clean kitchen along with some objectives like managing dishes and cleaning your stove. Would this guide to house cleaning be a curriculum?
Yes, but only if it includes accepted and relevant standards for what it means to have a clean house.
If “The Ultimate Guide to House Cleaning” was mostly dedicated to cleaning the garage or cellar, then it might not be relevant to those who do not have a garage or a cellar. Even if the “Ultimate Guide” included common rooms like kitchens and bathrooms, we may run into problems for those who live in studio apartments or have wide-open spaces.
This is where the broader and more universally relevant information comes in handy - like floors, surfaces, ceilings, and walls. Every room has floors, surfaces, ceilings, and walls, so if we created the “Ultimate Guide” to focus on universal information, then it would be helpful to almost everyone who owns a house - no matter what kinds of rooms they had.
No.
Let me repeat. No, Nay, Never. Never EVER.
It is not the function of a curriculum to prescribe how to teach. If someone thinks that a curriculum should tell you how to teach, then they are confused about the concept and function of a curriculum in a democratic society.
Curricula should steer completely clear of prescribing actions that a teacher should take. But why? Where's the harm?
The harm is in the specificity, because the more specific you get, the less freedom there is to innovate.
Also, the more specific you get, the more disagreement you will have. While teachers from all schools might agree that an important learning standard for algebra is factoring polynomials, they may not agree on the specific teaching methods. They may indeed use different methods.
Using broad guiding principles in a curriculum allows teachers some choice in their methods, giving them the opportunity to innovate and use their creativity. Stifling teaching with the mandate for specific types of teaching methods (unless these methods are required to meet the needs of students with learning problems) is harmful because it denies the dignity of teachers and indicates the lack of guiding principles.
In our house-cleaning curriculum analogy with math, we already learned that including "cleaning standards" for floors, surfaces, ceilings, and walls was more universally applicable - and therefore more useful - than guides for specific rooms. But we can get even more specific if we prescribe how to clean. Let’s say that the “Ultimate Guide to House Cleaning” included an objective like, “wipe down the stove with 12 heavy circular strokes using a lemon disinfectant spray that cuts grease.”
The specificity of the “12 heavy circular strokes” objective may work for some, but for others - they may already have a useful way to wipe down their stove that includes fewer strokes and less toxic, unscented spray. If the book, “The Ultimate Guide to House Cleaning” were designed with lots of prescriptive and specific advice, then it would be exclusive instead of inclusive.
The art and the science of teaching thrives when curricula are inclusive guides.
So back to the question - where's the harm in prescribing specific teaching methods? Ultimately, if certain methods work to meet the goals in a curriculum, then these methods should be taught and discussed in teacher prep programs, but not until all teachers understand the concept of a curriculum and why it's important in a democratic society.
Let's think about why a curriculum is important for schools.
Public (and some private) schools exist for one reason - to promote the greater good of a society. If a curriculum is designed too specifically, we get lost - we don't know if we’re improving math for the greater good of our society or if we’re improving math to support one individual’s vision of math - let’s say an influential teacher (like Dan Meyer), an educational leader (like Bill Gates), or a textbook publisher (like Pearson).
Keeping the "house cleaning" curriculum broad and focused on surfaces and floors is like keeping a math curriculum focused on inclusive concepts like proportional thinking and fraction sense.
But with too much inclusivity and not enough specificity, could we miss something? Should we be worried that the kitchen will ever actually be cleaned at all - or that we're not helping students learn math? Don’t worry - universally accepted curriculum standards are necessary guideposts to design assessments - and assessment, when done well, can ensure that broad, universal learning standards are being met.
Assessments are a set of methods that allow educators to gather information about how students are progressing toward these learning standards. Assessment is important because teaching has one purpose: to foster learning in students and ultimately improve the public good.
In our example of housecleaning - let's not forget about the ultimate goal - to have a clean house. I mean, come on - isn’t that why we’re doing all this, to ensure that our darn house is clean?
Getting back to math, aren't we teaching to ensure that students are learning, and are able to deal independently with more challenging math content?
Because our eyes are set on our ultimate goal - to ensure that children attain the most fundamental of knowledge in math - it’s important to have consensus and input from stakeholders (people who have a stake in the outcome) - like parents, teachers, and students.
Because a curriculum is the embodiment of public consensus (i.e., topics that are generally accepted in society as important to learn and teach), then good assessments can be designed using the topics in that curriculum. The goal of an assessment would be to decide if students need to learn more to attain mastery of a topic, or if they know enough about or are able to perform skills that certify their mastery.
With assessment, we gather information for a reason - to help us make a decision (and testing is a specific type of assessment - so is observation). One of the most important decisions that educators can make is whether or not students are attaining important outcomes.
With math or numeracy, like literacy, we want kids to learn math so that our society benefits. If math indeed is important to support a growing and thriving society, we need a way to know if we’ve done a good job teaching so that students have learned what teachers have taught.
Assessment therefore has a dual purpose: to help improve learning (assessment for learning) and to ensure that those who are in charge of teaching are accountable to those who learn from them (assessment of learning).
Oh, and by the way, if someone tells you that accountability isn't important, or that we don't need to hold schools accountable - run far and fast from them, because their vision is not of democracy but autocracy. We can have accountability and learning - it does not have to be a binary.
Although accountability is a fundamental part of democracy, at least in education, sometimes the testing can get out of hand. Unless we want to get caught in a rabbit hole, we should put this issue aside - but I think we can agree that assessment is important for accountability and for learning and teaching.
We've covered a few important topics. As we’ve learned, a curriculum is a carefully sequenced set of accepted topics (often known as standards) that can be translated into goals and objectives to guide teaching and learning. Curricula are important because they guide the creation of assessment tools, which educators use to ensure that we're on the right track. Here are a few questions to ponder as you learn about how to better advocate for an effective math curriculum for your kids and students:
Is a textbook a curriculum?
Is assessment important?
Should a curriculum prescribe how to teach?
How can curricula help to improve the public good?
Dr. Scott Methe is the owner of Mathnasium Learning Center in North Manchester, New Hampshire. Please contact Dr. Methe if you would like tutoring, consultation, or if you would like to schedule him to talk at your event. He can be reached at [email protected] or at 603-644-1234.
