Exploring Webb’s Depth of Knowledge

In order to more accurately analyze the types of questions offered in standardized assessments, Norman L. Webb developed a system called Depth of Knowledge. Rather than categorize questions by difficulty, this system categorizes them by complexity. In other words, questions are categorized by the type of thinking that is required to adequately answer them. This method allows assessments to be aligned more accurately with the standards they represent. The four categories are as follows:

The verbs shown in Webb’s image above are examples of words frequently found within each type of question. However, there are many exceptions and more information on how to identify and categorize assessment questions into the correct level of complexity is explored in this blog post, along with examples of each type of question.

Recall and Reproduction

The Wowzers curriculum embraces Webb’s Depth of Knowledge, and includes assessment questions from all four levels. The first category is “recall and reproduction.” Questions from this level require students to recall a fact, term, or procedure. When answering these types of questions, students are not required to do anything beyond remember a particular definition, type of computation, or formula. These questions often ask them to “define” or “compute” a basic fact or one-step calculation.

In this question, students are asked to recall a series of facts and procedures regarding integers. At this level, students must understand the information (they are not simply reciting information verbatim), but they are not yet using this information in a complex manner.

Skills and Concepts

At this second, more complex level, students are asked to use information or conceptual knowledge. These questions often have two or three steps. To answer the question, students must make a decision about how to approach the problem. It often requires them to organize, summarize, predict, or estimate.

In this question, students are asked to estimate the value of a series of square roots. This is a multi-step process that requires the student to analyze each number and go through a series of steps to correctly categorize it.

Strategic Thinking

In the next step of complexity, students must develop a plan to solve non-routine problems using multiple steps. There is sometimes more than one correct answer, and thinking is more abstract. Questions often ask students to justify their choices or support their ideas with details and examples.

In this question, students are asked to analyze a graph, consider how someone might find it misleading, and then describe their reasoning. This level of abstract thinking requires a higher depth of knowledge.

Extended Thinking

In this more complex type of question, questions require students to investigate and process multiple conditions or sources. These questions often take a much longer time to answer. Most assessments do not include questions of this complexity, and they are often instead included in projects and longer-term activities. To address these extended thinking questions, Wowzers includes offline activities that teachers can print out at any time.

In this assignment, students are asked to consider multiple conditions and go through a series of steps in order to solve a probability question. Because questions like this require a longer amount of time and text to thoroughly answer, Wowzers includes a similar assignment for each section of work, in addition to the daily and weekly assessments.

What are the Standards for Mathematical Practice?

The Standards for Mathematical Practice contain eight types of expertise that students should strive for. These standards stress the importance of understanding what a problem is asking, creating a solution using tools and models, and communicating this solution with peers. Skills such as problem-solving, reasoning, and using tools and models appropriately are important at all grade levels.

1. Make sense of problems and persevere in solving them.

Students must understand how to break apart problems into simpler pieces, plan how they intend to solve the problem, and continuously monitor their solution and ask themselves if it makes sense. After providing students with the basic skills to solve a problem, it’s important to build on this knowledge by asking questions that combine integral concepts in a word problem. Students also must learn how to compare ideas written in different ways. By fluidly moving between different forms of the same equation, students can make comparisons and decisions in real-world scenarios.

2. Reason abstractly and quantitatively.

Students must learn how to represent a situation symbolically with numbers and symbols, but they also must understand what that equation or process means in context. They should be able to translate a word problem into a mathematical process, then relate their answer back to the original context and include the correct units. By giving students problems in the context of a real-world scenario, they can learn to solve these problems using the math skills they are working on, then relate it back to the original problem.

 

 3. Construct viable arguments and critique the reasoning of others.

Students must learn how to formulate a conjecture and build a series of logical statements to support it. Arguments should be constructed logically, using definitions, rules, models, drawings, and diagrams. By comparing their reasoning and proof with peers, and evaluating each others’ arguments, students can decide which methods and solutions make sense, identify flawed logic, and improve their own skills.

4. Model with mathematics.

Incorporating a wide variety of models, such as tables, graphs, and diagrams, allows students to learn how to represent and visualize complicated situations. Students create and analyze these models to understand relationships and draw conclusions. It’s also important for students to understand when to use each type of model, and how to apply them to real situations. Students should learn how to choose an appropriate model and when one may be more useful than another.

5. Use appropriate tools strategically.

Students must learn how to choose an appropriate tool, how to read the tools with precision, and what the tools represent. By using tools to solve problems, students gain a deeper understanding of concepts, such as how to convert units from one system of measurement to another. Students must also make decisions on the best tool to use in different situations.

6. Attend to precision.

Students should understand and be able to use precise definitions when describing mathematical concepts and symbols. By carefully specifying unit of measure and labeling graphs appropriately, students are able to give a more accurate answer to problems, with less chance of misunderstanding. These terms and definitions should be used in students’ own writing as well.

7. Look for and make use of structure.

Recognizing patterns or structures is an important step in understanding many mathematical concepts. For example, by understanding multiplication as repeated addition, or the fact that 7 × 3 and 3 × 7 is the same answer, students begin to recognize rules and definitions. By showing ideas visually and allowing the students to interact with manipulatives, students often have an easier time seeing patterns.

 

8. Look for and express regularity in repeated reasoning.

Students who notice when they are performing a calculation repeatedly have an easier time recognizing general methods and shortcuts. For example, recognizing a repeated calculation is essential when determining whether a decimal is repeated or not. Identifying a function or pattern also relies on students recognizing repeated reasoning.

The Science of Learning

A lot of research has been done into the science of how we learn, but how does it relate to online, game-based learning?

Brain-based research emphasizes the fact that engagement must be the goal of all educators. When students are not engaged, their minds wander and learning isn’t effective. When engaged, students are excited to learn. Higher levels of engagement are associated with students who want to learn more and apply what they have learned in the real world.

Every brain is unique, which means strategies need to include a variety of activities that build not only declarative knowledge but also underlying cognitive skills. A great way to accomplish this is by including online activities that motivate this new generation of digital natives. Game-based learning improves knowledge along with a variety of cognitive skills, including memory, thinking, processing, sequencing, and attention.

Because people absorb information differently, generally through some combination of auditory, visual, and kinesthetic learning, blended learning programs should include activities that call for movement and a hands-on approach to learning that addresses the physical learning system of the brain.

Most students today have grown up with technology and, in a sense, demand the engaging content that they have grown accustomed to through online gaming. Students expect to receive immediate feedback and move at their own pace, which frees them from the fear of failing and satisfies both the cognitive and the emotional centers of the brain. The core online skills that students develop can then be applied to offline and online activities that focus on problem solving, communication, and creativity. 

Assessing student knowledge is the key to success. Today’s assessments typically include a variety of interactive manipulatives and tools.  Through practice, students can concentrate on answering the content questions without having to figure out how to manipulate the technology, giving us a clearer picture of what they know and don’t know.

These new types of questions can actually stand alone as learning tools for students. Different question types (such as extended response, sorting information, placing numbers on a number line, etc.) give us a much more accurate picture of what a student truly understands versus the old method of filling in a bubble.

Not only is digital, game-based learning fun for students, it’s also supported by research and provides endless opportunities for educators.

Reward Systems that Work

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Reward systems in the classroom are a valuable way for students to feel empowered in their progress and behavior. When implemented correctly, these rewards create a tangible way for students to see their progress and involves them as participants. However, reward systems that are too loose or inconsistent can encourage entitlement or resentment between students. Today, we explore what a successful reward system looks like.

Creating a Plan

The first step in implementing a reward system is deciding what behavior or milestones should be rewarded. They should be something achievable, but at a frequency that boosts motivation. For example, in Wowzers, students receive a small number of virtual coins for completing activities. A few coins are given just for their progress, but additional coins are rewarded if they answer questions correctly. This encourages students to continue working on the curriculum in order to make progress, but also to slow down and ensure they are truly understanding the material and answering questions correctly.

Frequency of Rewards

The frequency at which students should receive rewards often varies with age. While younger students need more frequent reminders and encouragement, older students can go longer between rewards. One common suggestion is that toddlers should be rewarded every hour, preschoolers should be rewarded every day, and school-age students should be rewarded every week. To support this theory, Wowzers allows teachers to manually reward students with extra coins whenever they wish. These larger rewards can be linked to things such as classroom behavior, timeliness, and remembering to bring supplies or homework to class.

Immediate Feedback

The most powerful reward systems give students immediate feedback. While an immediate reward is not necessary at most ages, as discussed above, students should know that their positive progress or behavior was recognized. In Wowzers, students receive a virtual coin immediately, but they are not able to spend it until they’re in the free time portion of the program. By immediately recognizing students, it creates a much stronger link between the desired behavior or progress and the reward. Students feel motivated and empowered and are more likely to continue the activity.

Variety of Rewards

Different students desire different types of rewards. Wowzers solves this problem with our virtual mall, which allows students to spend their coins on a huge variety of in-game goods. When creating your own reward system, you may want to allow students to choose their own reward. Some students might value being allowed to sit next to a friend while others want a sticker or a positive call home to their parents. Whatever the reward, being able to physically see their progress has been shown to work best. This can take the form of an invented currency or a positive behavior chart on the wall.

To learn more how the Wowzers K-8 online math program rewards students for learning, contact our team or try a free trial.

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The Next Step in Gamifying Learning

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When most teachers hear about gamifying learning, they think of games that double as a teaching tool or a classroom-made game of trivia to review concepts before a test. However, some schools have taken the concept of gamification to the next level, such as Quest to Learn in New York City. At this school, 100% of learning is posed as a game.

What it Looks Like

The school awards levels instead of grades, everything from “Novice” to “Master.” Even the subjects have more descriptive names. For example, science is re-dubbed “The Way Things Work.” Learning takes place through quests: a thematic unit where students have to work together to solve a series of challenges.

Some such quests ask students to invent a method of transport that could penetrate the Earth to its core, managing all the layers of the Earth in the process. In another quest, students work at a fictional biotech company, where they must clone dinosaurs and create a stable ecosystem for them. Technology is interwoven into everything they do. Using Storyweavers, a collaborative program, students work together to create stories. To practice math concepts, students might invent and play a new card game or be asked to design a structurally-sound building. In one class, students were asked to pick a real Supreme Court case, have the class argue both sides, while students assigned as judges are tasked with ensuring a fair and balanced decision.

How it Works

Designers of the curriculum have studied how to make engaging games. Challenge is constant and mistakes are only minor setbacks, easily overcome. Immediate feedback and rewards are vital, and learning requires participation and interaction. Technology is often integrated into the curriculum, allowing students to play the role of professionals, using role-playing games, graphics programs, and simulations to explore complex careers and situations.

The school is exceptionally popular, and students enroll through a lottery system. Around 650 students attend, spread out across middle school and high school. The students are still required to take the same standardized tests as other students across the country, but their prep is clearly much different.

Effectiveness of the Program

Student attendance and teacher retention rates are high at Quest to Learn. Clearly, the students seem to enjoy learning and going to school. The students’ test scores are fairly average for the area, receiving a solid 5 on GreatSchools. However, perhaps more importantly, the students are above average in problem-solving skills, being able to collaborate and think critically. They also receive much more insight into potential future careers than in a typical curriculum.

However, the system is not easy to implement. Quest to Learn receives hundreds of requests every week from other schools who want to use the curriculum. One Chicago school attempted to integrate the entire curriculum into their existing one, but failed to sufficiently train their staff. Teachers and students were both confused and the implementation was not successful.

Quest to Learn potentially shows the future of learning, where games are not just used in the classroom, but naturally integrated in all aspects.

To learn how the Wowzers K-8 online math program can help make learning fun, contact our team or try a free trial.

sales@wowzers.com

P: 872-205-6250

F: 888-502-2106

How Peer Pressure Affects Learning

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Anyone who has worked with students has likely seen the effects of peer pressure in schools. Whether it’s an individual being discouraged to take studying seriously or certain subjects in school being less “cool” to enjoy, peers’ opinions hold power. Now, new research shows exactly how much this power really affects students.

Peer Pressure in Action

SAT prep courses are a popular way for today’s students to gain an advantage on the SAT. In fact, students report that by taking a prep course, they expect their SAT score to go up by at least 100 points, which is fairly significant and would likely affect their college acceptance rate. To measure the power of peer pressure, the National Bureau of Economic Research offered SAT prep courses at several Los Angeles high schools. In the schools where the sign-ups were described as public, meaning that students’ peers could see who signed up, only 53% of students expressed interest in the course. In schools where the sign-ups were described as private, so that no one could see who had signed up, 80% of students wanted to participate.

This research suggests that around one-third of the students who wanted to take an SAT prep course would forgo signing up, just to “save face” among their peers. The results were particularly surprising because the majority of students wanted to take the prep course, but so many of them still hesitated, due to how their classmates would perceive their interest. Furthermore, even students in peer groups who valued education were hesitant to sign up for the prep classes publicly because of the perception that they needed academic assistance. The takeaway from this study is that peer pressure is in full effect in our schools, and can cause students to walk away from opportunities they would normally take.

Preventing Peer Pressure

Understanding how peer pressure affects students is one thing, but how do we respond to it? As the study showed, an overwhelming majority of the students were interested in taking an “uncool” prep class if their classmates didn’t know they were doing it. Students value privacy in their educational needs. This is why we at Wowzers allow students to work at their own pace, in different sections of the curriculum, and often in varying grade levels. Students are never informed if they are working at a slower pace or at a lower level than their classmates, and there is no way for others to see where their peers are at in the curriculum. This prevents peer pressure from taking effect, and allows students the privacy they clearly desire.

To learn how the Wowzers K-8 online math program eliminates peer pressure in learning, contact our team or try a free trial.

sales@wowzers.com

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Wowzers Now Available for Parents to Purchase

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For the first time ever, Wowzers is now available for parents to purchase for use at home!

Why Wowzers?

Wowzers Online Math is based on brain-based research and is designed to meet the needs of all learners. Children are able to fill in gaps in their learning or challenge themselves with more difficult concepts. With a varied, adaptive approach that includes lessons, games, quests, and assessments, Wowzers covers every math standard that your child needs to know from Kindergarten through 8th grade.

What’s included?

Whether you want to use Wowzers for homeschooling, as a summer program to prevent the summer slide, as intervention for a child who struggles with math, for a gifted and talented child who need a challenge, or as a supplement to an in-school program, a subscription includes a full year of digital content for each grade level. The program is highly flexible and it’s possible to move children down a grade if the curriculum is too difficult, or up a grade for more challenging content.

How do children and parents access the content?

Parents create an account, then generate a login for each child they want to access Wowzers. Children automatically begin at the start of the grade level assigned to them and progress naturally through the curriculum, but can choose to skip to other math content within their grade level if desired. We will be rolling out more reporting tools for parents to keep tabs on their child’s progress soon!

What is the cost?

Apply today for a 7-day free trial. If you like what you see, we offer two subscription plans:

  • Monthly plan: $14.99/child
  • Yearly plan: $149.99/child (17% savings)

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Tips on Securing Funding for New Technology

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There’s no shortage of innovative technology solutions that support strategies such as personalized learning and effective teaching strategies, but the cost can quickly become prohibitive. With tightening school budgets and personal spending accounts only going so far, what other funding sources are available for teachers?

Donor Programs

One possibility is to create a project through a donor program, such as DonorsChoose.org. This website allows the public to search for a project that they want to support through donations. Teachers create a page that describes their project, upload pictures, and set a goal. Each submission is vetted by staff to verify that the goal is fair and the project is well-explained. Donations are tax-deductible and because each project receives its own URL, it’s easy to share with others through social media or email. Over 75% of teachers reach their goal, and once funded, DonorsChoose.org takes care of ordering and shipping all the materials directly to the school. Before submitting your own project, we recommend browsing through some successful examples to get an idea of what works.

Grants

The other major source of funding for teachers is through grants. Many sites exist that search all currently offered grants for a particular topic or area. For example, grants.gov allows users to search by keyword and includes thousands of available grants. To find education-specific grants, sites such as Grants for Teachers or Get Ed Funding are good options as well. To apply for a grant, simply follow the instructions to create a proposal that describes why your classroom needs the funds and how they would be used. For tips on how to write a successful grant, check out these tips and resources. If you have a particular program you want to implement, their staff may also be willing to help you put together the proposal.

For more info on the Wowzers K-8 online math program, contact our team or try a free trial

sales@wowzers.com

P: 872-205-6250

F: 888-502-2106

Surge in Innovation with ESSA

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One of the main criticisms of the No Child Left Behind Act was that it put too much focus on preparing students to take assessments, limiting schools’ ability to innovate and try new ways of teaching content. Teachers stuck with what they knew, fearing the risk of failure and the associated sanctions. However, this outdated act was replaced in 2015 with the Every Student Succeeds Act (ESSA), which has opened the doors to innovation.

ESSA Changes

ESSA gives much of the power back to the states and school districts. Although students continue to participate standardized testing, each state is now responsible for putting together plans on how to help students succeed, how to evaluate schools, and how to respond to schools that do poorly. As a result, teachers no longer have to fear the federal government stepping in to fire staff and close schools if their students struggle on these assessments.

Increase in Innovation

In the short amount of time that ESSA has been in effect, innovation in education has become a huge part of the conversation in schools. States have begun submitting their education plans, and many of them include a focus on personalized learning. New Jersey, for example, plans to provide professional development related to personalized learning and offer grants to schools that want to provide personalized instruction. Virginia also emphasizes innovation in their plans, as they allow schools to apply for waivers from requirements that would limit their ability to innovate.

Sharing Success Stories

As research continues to emerge about how powerful personalized learning can be for students, ESSA finally allows schools to pursue these new possibilities without as much fear. New Hampshire has asked teachers to document their unique intervention strategies and how they work, recognizing that their teachers are experts in teaching and often have revolutionary ideas on how to make learning more effective. This will allow teachers to pursue new technology and personalized learning solutions, while also sharing their findings with others.

For detailed strategies on how schools can innovate with ESSA and prepare for accountability requirements, we recommend this comprehensive handbook, published by the Center for Digital Education.

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To learn how Wowzers K-8 Online Math program can help schools innovate and make learning math fun, contact our team or try a free trial

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Is Math Still an Important Skill to Learn?

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We’ve all heard the complaints from students about how they don’t believe math will be useful in their lives after school, but what about their parents? How do they value math as a subject worth learning, particularly in relation to other skills?

Survey Results

A recent survey of more than 2500 parents found that over a third of them believe that math is only useful for people going into math-related careers, so the average American doesn’t have much need for math. Researchers also noted that the parents tended to value reading skills over math. This creates an issue for teachers who must overcome this mindset from both students and their parents to not only teach math skills, but also teach the value of math in everyday life.

Early Math Skills

While most of the emphasis on early learning has been on reading, researchers have found that early math skills are just as important to long-term success. They believe the reason for this disconnect is two-fold: first, it’s much easier for programs to encourage parents to pick up a book to read with their child. Libraries can easily support this message as well. Second, there is a culture of anxiety around math in America. It’s much more culturally acceptable for people to claim they’re “just not a math person” than admitting that they can’t read well. Parents often have bad memories of not understanding math when they were younger, and the way math is taught changes often, with little visibility to parents. For these reasons, math is often left to schools with little support from home, or in early years.

Changing the Perception

As mentioned earlier, math skills are crucial from a young age. One long-term study found that math skills at the beginning of kindergarten were the best predictor of academic skills in eighth grade. In order to encourage parents to start working on math skills with their young children, it’s important for those who work with young children—such as kindergarten and preschool teachers—to explain to parents how to talk about math with their children. Activities from estimating the number of fish in a tank at the pet store to looking for patterns in the tiles laid out on the floor can strengthen early math skills. For teachers of older students, reinforcing the importance of math skills such as logical reasoning and critical thinking can help parents understand why math is such a crucial skill for everyone, not just those going into math-related careers.

To learn how Wowzers K-8 Online Math program can make learning engaging and open a math dialogue between students and their parents or teachers, contact our team or try a free trial

sales@wowzers.com

P: 872-205-6250

F: 888-502-2106