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Unlocking the Power of Math Learning: Strategies and Tools for Success

posted on September 20, 2023

Mathematics, the foundation of all sciences and technology, plays a fundamental role in our everyday lives. Yet many students find the subject challenging, causing them to shy away from it altogether. This reluctance is often due to a lack of confidence, a misunderstanding of unclear concepts, a move ahead to more advanced skills before they are ready, and ineffective learning methods. However, with the right approach, math learning can be both rewarding and empowering. This post will explore different approaches to learning math, strategies for success, and cutting-edge tools to help you achieve your goals.

Math Learning

Math learning can take many forms, including traditional classroom instruction, online courses, and self-directed learning. A multifaceted approach to math learning can improve understanding, engage students, and promote subject mastery. A 2014 study by the National Council of Teachers of Mathematics found that the use of multiple representations, such as visual aids, graphs, and real-world examples, supports the development of mathematical connections, reasoning, and problem-solving skills.

Moreover, the importance of math learning goes beyond solving equations and formulas. Advanced math skills are essential for success in many fields, including science, engineering, finance, health care, and technology. In fact, a report by Burning Glass Technologies found that 71% of high-salary, entry-level positions require advanced math skills.

Benefits of Math Learning

In today’s 21st-century world, having a broad knowledge base and strong reading and math skills is essential. Mathematical literacy plays a crucial role in this success. It empowers individuals to comprehend the world around them and make well-informed decisions based on data-driven understanding. More than just earning good grades in math, mathematical literacy is a vital life skill that can open doors to economic opportunities, improve financial management, and foster critical thinking. We’re not the only ones who say so:

• Math learning enhances problem-solving skills, critical thinking, and logical reasoning abilities. (Source: National Council of Teachers of Mathematics )
• It improves analytical skills that can be applied in various real-life situations, such as budgeting or analyzing data. (Source: Southern New Hampshire University )
• Math learning promotes creativity and innovation by fostering a deep understanding of patterns and relationships. (Source: Purdue University )
• It provides a strong foundation for careers in fields such as engineering, finance, computer science, and more. These careers generally correlate to high wages. (Source: U.S. Bureau of Labor Statistics )
• Math skills are transferable and can be applied across different academic disciplines. (Source: Sydney School of Education and Social Work )

How to Know What Math You Need to Learn

Often students will find gaps in their math knowledge; this can occur at any age or skill level. As math learning is generally iterative, a solid foundation and understanding of the math skills that preceded current learning are key to success. The solution to these gaps is called mastery learning, the philosophy that underpins Khan Academy’s approach to education .

Mastery learning is an educational philosophy that emphasizes the importance of a student fully understanding a concept before moving on to the next one. Rather than rushing students through a curriculum, mastery learning asks educators to ensure that learners have “mastered” a topic or skill, showing a high level of proficiency and understanding, before progressing. This approach is rooted in the belief that all students can learn given the appropriate learning conditions and enough time, making it a markedly student-centered method. It promotes thoroughness over speed and encourages individualized learning paths, thus catering to the unique learning needs of each student.

Students will encounter mastery learning passively as they go through Khan Academy coursework, as our platform identifies gaps and systematically adjusts to support student learning outcomes. More details can be found in our Educators Hub . 

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How to learn math.

Learning at School

One of the most common methods of math instruction is classroom learning. In-class instruction provides students with real-time feedback, practical application, and a peer-learning environment. Teachers can personalize instruction by assessing students’ strengths and weaknesses, providing remediation when necessary, and offering advanced instruction to students who need it.

Learning at Home

Supplemental learning at home can complement traditional classroom instruction. For example, using online resources that provide additional practice opportunities, interactive games, and demonstrations, can help students consolidate learning outside of class. E-learning has become increasingly popular, with a wealth of online resources available to learners of all ages. The benefits of online learning include flexibility, customization, and the ability to work at one’s own pace. One excellent online learning platform is Khan Academy, which offers free video tutorials, interactive practice exercises, and a wealth of resources across a range of mathematical topics.

Moreover, parents can encourage and monitor progress, answer questions, and demonstrate practical applications of math in everyday life. For example, when at the grocery store, parents can ask their children to help calculate the price per ounce of two items to discover which one is the better deal. Cooking and baking with your children also provides a lot of opportunities to use math skills, like dividing a recipe in half or doubling the ingredients. 

Learning Math with the Help of Artificial Intelligence (AI) 

AI-powered tools are changing the way students learn math. Personalized feedback and adaptive practice help target individual needs. Virtual tutors offer real-time help with math concepts while AI algorithms identify areas for improvement. Custom math problems provide tailored practice, and natural language processing allows for instant question-and-answer sessions. 

Using Khan Academy’s AI Tutor, Khanmigo

Transform your child’s grasp of mathematics with Khanmigo , the 24/7 AI-powered tutor that specializes in tailored, one-on-one math instruction. Available at any time, Khanmigo provides personalized support that goes beyond mere answers to nurture genuine mathematical understanding and critical thinking. Khanmigo can track progress, identify strengths and weaknesses, and offer real-time feedback to help students stay on the right track. Within a secure and ethical AI framework, your child can tackle everything from basic arithmetic to complex calculus, all while you maintain oversight using robust parental controls.

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Math learning is essential for success in the modern world, and with the right approach, it can also be enjoyable and rewarding. Learning math requires curiosity, diligence, and the ability to connect abstract concepts with real-world applications. Strategies for effective math learning include a multifaceted approach, including classroom instruction, online courses, homework, tutoring, and personalized AI support. 

So, don’t let math anxiety hold you back; take advantage of available resources and technology to enhance your knowledge base and enjoy the benefits of math learning.

National Council of Teachers of Mathematics, “Principles to Actions: Ensuring Mathematical Success for All” , April 2014

Project Lead The Way Research Report, “The Power of Transportable Skills: Assessing the Demand and Value of the Skills of the Future” , 2020

Page. M, “Why Develop Quantitative and Qualitative Data Analysis Skills?” , 2016

Mann. EL, Creativity: The Essence of Mathematics, Journal for the Education of the Gifted. Vol. 30, No. 2, 2006, pp. 236–260, http://www.prufrock.com ’

Nakakoji Y, Wilson R.” Interdisciplinary Learning in Mathematics and Science: Transfer of Learning for 21st Century Problem Solving at University ”. J Intell. 2020 Sep 1;8(3):32. doi: 10.3390/jintelligence8030032. PMID: 32882908; PMCID: PMC7555771.

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Encyclopedia of Mathematics Education pp 159–163 Cite as

Critical Thinking in Mathematics Education

• Eva Jablonka 2  
• Reference work entry
• First Online: 01 January 2020

826 Accesses

8 Citations

Mainstream educational psychologists view critical thinking (CT) as the strategic use of a set of reasoning skills for developing a form of reflective thinking that ultimately optimizes itself, including a commitment to using its outcomes as a basis for decision-making and problem solving. In such descriptions, CT is established as a general methodological standard for making judgments and decisions. Accordingly, some authors also include a sense for fairness and the assessment of practical consequences of decisions as characteristics (e.g., Paul and Elder 2001 ). This conception assumes rational, autonomous subjects who share a common frame of reference for representation of facts and ideas, for their communication, as well as for appropriate (morally “good”) action. Important is the difference as to what extent a critical examination of the criteria for CT is included in the definition: If education for CT is conceptualized as instilling a belief in a more or less fixed...

• Logical thinking
• Argumentation
• Deductive reasoning
• Mathematical problem solving
• Mathematical literacy
• Critical judgment
• Goals of mathematics education

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Appelbaum P, Davila E (2009) Math education and social justice: gatekeepers, politics and teacher agency. In: Ernest P, Greer B, Sriraman B (eds) Critical issues in mathematics education. Information Age, Charlotte, pp 375–394

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Pimm D (1990) Mathematical versus political awareness: some political dangers inherent in the teaching of mathematics. In: Noss R, Brown A, Dowling P, Drake P, Harris M, Hoyles C et al (eds) Political dimensions of mathematics education: action and critique. Institute of Education, University of London, London

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Jablonka, E. (2020). Critical Thinking in Mathematics Education. In: Lerman, S. (eds) Encyclopedia of Mathematics Education. Springer, Cham. https://doi.org/10.1007/978-3-030-15789-0_35

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Engaging Maths

Dr catherine attard, promoting creative and critical thinking in mathematics and numeracy.

• by cattard2017
• Posted on June 25, 2017

What is critical and creative thinking, and why is it so important in mathematics and numeracy education?

Numeracy is often defined as the ability to apply mathematics in the context of day to day life. However, the term ‘critical numeracy’ implies much more. One of the most basic reasons for learning mathematics is to be able to apply mathematical skills and knowledge to solve both simple and complex problems, and, more than just allowing us to navigate our lives through a mathematical lens, being numerate allows us to make our world a better place.

The mathematics curriculum in Australia provides teachers with the perfect opportunity to teach mathematics through critical and creative thinking. In fact, it’s mandated. Consider the core processes of the curriculum. The Australian Curriculum (ACARA, 2017), requires teachers to address four proficiencies : Problem Solving, Reasoning, Fluency, and Understanding. Problem solving and reasoning require critical and creative thinking (). This requirement is emphasised more heavily in New South wales, through the graphical representation of the mathematics syllabus content , which strategically places Working Mathematically (the proficiencies in NSW) and problem solving, at its core. Alongside the mathematics curriculum, we also have the General Capabilities , one of which is Critical and Creative Thinking – there’s no excuse!

Critical and creative thinking need to be embedded in every mathematics lesson . Why? When we embed critical and creative thinking, we transform learning from disjointed, memorisation of facts, to sense-making mathematics. Learning becomes more meaningful and purposeful for students.

How and when do we embed critical and creative thinking?

There are many tools and many methods of promoting thinking. Using a range of problem solving activities is a good place to start, but you might want to also use some shorter activities and some extended activities. Open-ended tasks are easy to implement, allow all learners the opportunity to achieve success, and allow for critical thinking and creativity. Tools such as Bloom’s Taxonomy and Thinkers Keys  are also very worthwhile tasks. For good mathematical problems go to the nrich website . For more extended mathematical investigations and a wonderful array of rich tasks, my favourite resource is Maths300   (this is subscription based, but well worth the money). All of the above activities can be used in class and/or for homework, as lesson starters or within the body of a lesson.

Will critical and creative thinking take time away from teaching basic concepts?

No, we need to teach mathematics in a way that has meaning and relevance, rather than through isolated topics. Therefore, teaching through problem-solving rather than for problem-solving. A classroom that promotes and critical and creative thinking provides opportunities for:

• higher-level thinking within authentic and meaningful contexts;
• complex problem solving;
• open-ended responses; and
• substantive dialogue and interaction.

Who should be engaging in critical and creative thinking?

Is it just for students? No! There are lots of reasons that teachers should be engaged with critical and creative thinking. First, it’s important that we model this type of thinking for our students. Often students see mathematics as black or white, right or wrong. They need to learn to question, to be critical, and to be creative. They need to feel they have permission to engage in exploration and investigation. They need to move from consumers to producers of mathematics.

Secondly, teachers need to think critically and creatively about their practice as teachers of mathematics. We need to be reflective practitioners who constantly evaluate our work, questioning curriculum and practice, including assessment, student grouping, the use of technology, and our beliefs of how children best learn mathematics.

Critical and creative thinking is something we cannot ignore if we want our students to be prepared for a workforce and world that is constantly changing. Not only does it equip then for the future, it promotes higher levels of student engagement, and makes mathematics more relevant and meaningful.

How will you and your students engage in critical and creative thinking?

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20 Math Critical Thinking Questions to Ask in Class Tomorrow

• November 20, 2023

The level of apathy towards math is only increasing as each year passes and it’s up to us as teachers to make math class more meaningful . This list of math critical thinking questions will give you a quick starting point for getting your students to think deeper about any concept or problem. 

Since artificial intelligence has basically changed schooling as we once knew it, I’ve seen a lot of districts and teachers looking for ways to lean into AI rather than run from it.

The idea of memorizing formulas and regurgitating information for a test is becoming more obsolete. We can now teach our students how to use their resources to make educated decisions and solve more complex problems.

With that in mind, teachers have more opportunities to get their students thinking about the why rather than the how.

Table of Contents

Looking for more about critical thinking skills? Check out these blog posts:

• Why You Need to Be Teaching Writing in Math Class Today
• How to Teach Problem Solving for Mathematics
• Turn the Bloom’s Taxonomy Verbs into Engaging Math Activities

What skills do we actually want to teach our students?

As professionals, we talk a lot about transferable skills that can be valuable in multiple jobs, such as leadership, event planning, or effective communication. The same can be said for high school students. 

It’s important to think about the skills that we want them to have before they are catapulted into the adult world. 

Do you want them to be able to collaborate and communicate effectively with their peers? Maybe you would prefer that they can articulate their thoughts in a way that makes sense to someone who knows nothing about the topic.

Whatever you decide are the most essential skills your students should learn, make sure to add them into your lesson objectives.

When should I ask these math critical thinking questions?

Critical thinking doesn’t have to be complex or fill an entire lesson. There are simple ways that you can start adding these types of questions into your lessons daily!

Start small

Add specific math critical thinking questions to your warm up or exit ticket routine. This is a great way to start or end your class because your students will be able to quickly show you what they understand. 

Asking deeper questions at the beginning of your class can end up leading to really great discussions and get your students talking about math.

Add critical thinking questions to word problems

Word problems and real-life applications are the perfect place to add in critical thinking questions. Real-world applications offer a more choose-your-own-adventure style assignment where your students can expand on their thought processes. 

They also allow your students to get creative and think outside of the box. These problem-solving skills play a critical role in helping your students develop critical thinking abilities.

Keep reading for math critical thinking questions that can be applied to any subject or topic!

When you want your students to defend their answers.

• Explain the steps you took to solve this problem
• How do you know that your answer is correct?
• Draw a diagram to prove your solution.
• Is there a different way to solve this problem besides the one you used?
• How would you explain _______________ to a student in the grade below you?
• Why does this strategy work?
• Use evidence from the problem/data to defend your answer in complete sentences.

When you want your students to justify their opinions

• What do you think will happen when ______?
• Do you agree/disagree with _______?
• What are the similarities and differences between ________ and __________?
• What suggestions would you give to this student?
• What is the most efficient way to solve this problem?
• How did you decide on your first step for solving this problem?

When you want your students to think outside of the box

• How can ______________ be used in the real world?
• What might be a common error that a student could make when solving this problem?
• How is _____________ topic similar to _______________ (previous topic)?
• What examples can you think of that would not work with this problem solving method?
• What would happen if __________ changed?
• Create your own problem that would give a solution of ______________.
• What other math skills did you need to use to solve this problem?

Let’s Recap:

• Rather than running from AI, help your students use it as a tool to expand their thinking.
• Identify a few transferable skills that you want your students to learn and make a goal for how you can help them develop these skills.
• Add critical thinking questions to your daily warm ups or exit tickets.
• Ask your students to explain their thinking when solving a word problem.
• Get a free sample of my Algebra 1 critical thinking questions ↓

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7 thoughts on “20 math critical thinking questions to ask in class tomorrow”.

I would love to see your free math writing prompts, but there is no place for me to sign up. thank you

Ahh sorry about that! I just updated the button link!

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A Powerful Rethinking of Your Math Classroom

We look at strategies you can reset this year—adjusting your testing regimen, tackling math anxiety, encouraging critical thinking, and fostering a mistake-friendly environment.

The beginning of school is a great time for teachers—both veteran and early career—to consider ways they can improve upon their classroom practices over the next year. This may be especially important for math teachers, who often spend the early days of the school year confronting math anxiety , convincing students that they are indeed “math people,” and coming up with engaging practices to guide students to find pleasure in math challenges. Innovating in these areas has the potential to yield big benefits for students all year long.

To help you re-imagine some of your teaching practices this year, we’ve pulled together a collection of big and small strategies aimed at:

• helping students adopt a more productive, curious mindset when they approach math,
• engaging students as soon as they walk through the door,
• rethinking how you handle testing,
• fostering a mistake-friendly environment,
• incorporating humanities-style discussions into math, and
• building what Peter Liljedahl calls a “ thinking classroom .”

Tackle Negative Math Mindsets

“Most of my work as a math teacher isn’t even math ,” former middle school math teacher José Vilson has said. “It’s helping students believe that they can also do math.”

Striking a similar note, middle school math coordinator Alessandra King writes that supporting students—particularly students from marginalized backgrounds—to develop a “ positive mathematical identity ” is crucial to fostering a sense of belonging in a larger math community, boosting “their willingness and ability to engage” in challenging work.

King recommends spending the first few days of the school year spotlighting mathematicians from the past who reflect the makeup of your classroom. In her all-girls school, for example, she has students read and respond to a play about the achievements and struggles of Maria Agnesi, Sofya Kovalevskaya, and Emmy Noether, three historical female mathematicians. You can also hang up posters of famous Black or Latino mathematicians—such as Euphemia Haynes, the first African American woman to earn a PhD in math, or Robert Luis Santos, a Latino statistician and director of the U.S. Census Bureau—and devote lessons to discussing their achievements and backgrounds.

To get students thinking about—and challenging—their own math identity, educator Rolanda Baldwin suggests asking students early in the year to write a “ math autobiography .” They might respond to questions like: “How do you feel about math? How did your relationship with math change over time?” To draw students closer together—and make them realize that many students, of all backgrounds, struggle—have them share their responses in groups, or with the entire class.

Sometimes, our best intentions can go awry. Rachel Fuhrman, a former special education math teacher, notes that teachers can sometimes dampen a student’s math identity by wheeling out phrases that might seem helpful but can actually demotivate students , like: “This is so easy.” Framing something as “easy,” she writes, can leave students feeling uncomfortable or afraid of asking crucial, clarifying questions.

Engage Students the Moment They Enter the Classroom

To set a playful tone and lower the stakes of the work so students can effectively experiment and collaborate, high school math teacher Lorenzo Robinson suggests starting off class with fun, challenging brain teasers .

For example, ask students to draw a cross on a sheet of paper (you should draw one on the board as a point of reference). Ask students to draw two straight lines that will segment or cut the cross into pieces. The goal is to cut the cross in a way that produces the most pieces .

You could also try math riddles: Ask students to imagine they have two coins that total 30 cents. Tell them that one of the coins is not a nickel, and ask them to figure out what the two coins are.

Robinson finds that brain teasers like these can get students primed for problem solving and critical thinking, without even realizing it.

Lower the Stakes of Testing

Big tests—centered around units or near the end of a grading period—are staples of many math classrooms. But that doesn’t mean they have to be the only opportunity for students to show what they know. One way to lower the stakes for students and give them more opportunities to practice, while providing yourself more of an opportunity to both teach content and check for understanding is to give short assessments on a regular schedule. 

Math coordinator Steven Goldman’s school switched from tests to checkpoints . These short assessments include a mix of current and past topics—retrieval practice is a research-backed way to support greater learning , after all—with some repetition for the most important skills students need to know. The checkpoints are given every two weeks and are not formally graded, but mistakes are noted and teachers leave feedback to guide student revisions. The change, Goldman writes, resulted in a big reduction in student stress levels—something research shows is a benefit of frequent practice tests, alongside a boost in long-term retention. Because the checkpoints happen all the time, Goldman and his colleagues don’t have to “go through all kinds of contortions to finish a unit before a break or on a Thursday so that we could give the test at the right time.”

Fresno State math instructor Howie Hua suggests lowering the stake in your classroom by allowing students to discuss a test before starting to work on it . Hua recommends having students put their pencils on the floor so they can focus on their discussion. Hand out the test and give students five minutes to discuss strategies they can use to solve the problems. 

Good Mistakes, Better Mistakes

Mistakes are bound to happen in any math classroom, and how you respond to them throughout the year can make a world of difference. Making light of your own mistakes is a good first gambit, but research suggests a more advanced approach: Giving students space to make mistakes—and opportunities to analyze and discuss them with peers—can better encode information in their brains than simply providing them with the correct answer.

To use mistakes as building blocks to better solutions, math teacher Emma Chiapetta uses an ingenious, small-group activity that asks students to identify and reflect on common mistakes , and then explain the rationale behind them to their peers. Here’s how it works: Randomly separate students into groups and assign each group to a board to generate a problem and solve it incorrectly. Groups rotate so they’re looking at a problem and an incorrect solution, and have to identify the error and solve the problem correctly. After another rotation—so students are looking at a problem and both the incorrect and correct solutions—they explain to the class the mistake made by the first group and the correct solution provided by the second. The activity, Chiapetta writes, helps students think about the same content from various perspectives, which can lead to deeper understanding.

Not all mistakes are created equal, and they often conceal thoughtful, underlying work. Former math teacher Colin Seale asks students to reflect on which wrong answer to a problem is “ more right .” He suggests offering students two equations that are both incorrect—perhaps one is wrong conceptually and the other computationally. Seale notes that this exercise gets students to tease out nuances around the skills and concepts they’re learning, while also correcting their approach to similar problems moving forward.

Bring Humanities Strategies to Math Class

The discussion, analysis of reasoning, and argumentation that happen in humanities classrooms can be extremely useful in math classrooms to help students slow down and think through the work they’re doing , says middle school math teacher Connell Cloyd. 

He does this in his classroom by posting four incorrectly solved math problems around the room and having students rotate around each problem in groups to discuss the error and write down (in complete sentences) a claim and supporting evidence to show why they believe the error occurred. As they rotate around, students read the arguments of peers and either support an argument or refute it with new evidence. This is like adding techniques from debate to Chiappetta’s strategy.

Math journals can also inject more writing and reasoning into your classroom. Former math teacher Nell McAnelly prompts students to reflect on concepts they’re having trouble with : They work through a problem and then write about the strategy they used to solve it, or informally journal about other approaches they could have used. Doing so, she writes, gives students a chance to “synthesize learning and address unanswered questions.”

Driving Deep, Critical Thinking

A traditional math classroom, where the teacher demonstrates a skill numerous times before students take the reins, can inhibit higher order thinking and result in students who “mimic” teachers rather than develop their own strategies to solve complex problems , says Peter Liljedahl, a researcher and professor of mathematics at Simon Fraser University. 

Instead of starting lessons with direct instruction, Liljedahl says, give students novel “ thinking tasks ” to work on in groups. These are problem-solving activities and mental puzzles that should get students in the mindset of challenging themselves. Work groups should not be chosen based on ability or students’ preferences—Liljedahl’s research shows that students are more likely to contribute in randomized groups. Having students stand while they engage in this collaborative, messy thinking—as Chiappetta does in her mistake-analysis exercise—is another way to engage them.

Instead of using notebooks to compute, Liljedahl calls for groups to work at vertical, non-permanent surfaces, such as whiteboards, blackboards, or windows—surfaces that he says promote more risk-taking because students have the freedom to quickly erase false starts without feeling committed. As students work in groups, teachers bounce around the room and avoid directly answering questions such as “Is this right?” that circumvent student thinking and instead make suggestions that lead to further independent thinking. 

Because the goal of this approach is to get students to develop perseverance, curiosity, and collaboration, Liljedahl suggests evaluating them in a way that prioritizes these competencies. He developed formative assessments that focus on informing students “about where they are and where they’re going in their learning.” These include observations, check-for-understanding questions, and unmarked quizzes. Summative assessments, meanwhile, should focus less on end products and more on the process of learning through both group and individual work.

Shifting to this thinking classroom model requires a fundamental shift in how you run your classroom, but it could result in large rewards throughout the year.

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“Critical thinking relies on content, because you can't navigate masses of information if you have nothing to navigate to.” -Dr. Kathy Hirsh-Pasek, Professor of Psychology, Temple University

One of the most sought-after skills in nearly every workplace is critical thinking (Doyle, 2018, October 30). But what is critical thinking, exactly? Better yet … what does it take to think critically? To some, it is the ability to analyze information objectively and make a reasoned judgment; for others, it simply involves thinking “outside-the-box”. Either way, to think critically is to possess the unique ability to think reflectively and independently in order to make thoughtful decisions (Figliuolo, 2016, August 2). In other words, critical thinking is not just the accumulation of facts and knowledge; rather, it’s a process of approaching whatever is on your mind in order to come up with the best possible conclusion (Patel, 2018, October 24). Figure 1 illustrates the critical thinking process.

Figure 1. Critical thinking process

Three Essential Skills

To think critically, it begins with three essential skills:

• linking ideas,
• structuring arguments, and
• recognizing incongruences.

In order for you to become a better critical thinker, each of the three skills needs to be practiced and applied accordingly. The first skill, linking ideas, involves finding connections between seemly unrelatable, even irrelevant ideas, thoughts, etc. The second skill involves creating structured practical, relevant, and sound arguments. Lastly, to recognize incongruences is to find the real truth by being able to find holes in a theory or argument (MindValley, n.d.).

Food for Thought “No problem can withstand the assault of sustained thinking.” -Voltaire, French philosopher

Six Low-Level Questions

Once you have the three essential skills down, then you can ask yourself six low-level questions that you can use in nearly any situation (TeachThought Staff, 2018, July 29):

• What’s happening? Here, you will need to establish the basics and begin forming questions.
• Why is it important? Ask yourself why the situation at hand is or is not significant.
• What don’t I see? Ask yourself whether or not there is any important information you might be missing.
• How do I know? Ponder on not only how you know what you think you know, but how that thought process was generated.
• Who is saying it? Identify the speaker and their position on the situation, then consider how that position could be influencing that person’s thinking.
• What else? What if? Think of anything else you be considering when making your decision. In addition, ponder the repercussions of what you’ve considered that might change/alter the outcome of your decision.

Food for Thought “Learn to use your brain power. Critical thinking is the key to creative problem solving in business.” -Richard Branson, Entrepreneur

In order to better understand higher-level critical thinking, it helps to be familiar with Bloom’s Taxonomy, a classification of educational objectives and skills that educators establish for their students. In Bloom’s Taxonomy, there are three overarching domains known as KSA: (a) Knowledge [cognitive], (b) Skills [psychomotor], and (c) Attitudes [affective]. This taxonomy of learning behaviors is referred to as “the goals of the learning process.” In other words, after a period of learning, the student will have acquired a new knowledge, skill and/or attitude (Bloom et al., 1956). In this resource, we will focus on the Knowledge (cognitive) domain. According to Bloom et al. (1956), the cognitive domain involves the development of intellectual skills. There are six major categories of the cognitive process (Figure 2), beginning with the development with the simplest skills (e.g., remembering basic facts and concepts), through a learning of procedural patterns and concepts that facilitate the development of intellectual abilities, before eventually moving to the highest, most complex skills (e.g., creation of new or original ideas).

Figure 2. Bloom's Taxonomy

• To further explain, the first level of Bloom’s Taxonomy involves remembering specific information. This includes recalling basic vocabulary, dates, and math facts.
• Moving up the taxonomy, understanding is demonstrated by a student’s ability to comprehend, organize, compare and to verbalize main concepts. At this level, questions require the ability to understand meaning, not just basic facts. For example, a study might be asked to explain the difference between apples and oranges.
• The third level, application, is being able to actually use the new knowledge. Within this level, questions often require the student taking what s/he just learned, then applying it in a different way. For example, the student may be asked to take a list of food items, then select four items to make a healthy breakfast.
• The next level, analysis, involves breaking down information into different parts for a more thorough examination. Here, questions require proven facts (evidence) to support the answer. For example, the student is asked to compare and contrast Republicans to Democrats with regard to their views on supporting or repealing the Affordable Care Act.
• Evaluation, the fifth level, is the ability to make judgments about information by presenting and defending one’s own opinions. It is important to note that at this level, questions don’t necessarily have a right (or wrong) answer. For example, a student may be asked how s/he would handle observing a friend who cheated on a final exam.
• The top of the taxonomy involves the synthesis of new information and compiling it in new ways. It is at this level where more abstract, creative, “outside-the-box” thinking comes into play. For example, a student may be asked to design and construct a robot that can walk a certain distance.

While the first three levels of the taxonomy are important to solidify core knowledge, it is within the last three levels – analysis, evaluation, and creativity – that require critical thinking skills. (Anderson et al., 2001).

Practice Activity

In a study by Gottfried and Shearer (2016, May 26), the authors stated that 62% of adults get their news from social networking sites. In fact, the results show that 70% of Reddit users, 66% of Facebook users, and 59% of Twitter users get their news from one or more of these platforms. According to the study, among these three social networking sites, Facebook had the greatest reach with 67% of American adults using the platform. This suggests that the two-thirds of adults who use Facebook to get their news, which amount to 44% of the general population. Unfortunately, social media platforms don’t go through the stringent review process to which most major news outlets are required in order to be in compliance with Federal Communications Commission (FCC) regulations. Therefore, information can be shared publicly without “fact-checking” to make sure that what’s being shared is truly accurate. With this in mind, one can’t help but ask: What’s the truth versus what isn’t? Better yet … what’s real news and what’s fake?

Your task involves the use of Bloom’s Taxonomy to decipher “fake news” from real news. Using the eight-step infographic on the International Federation of Library Associations and Institutions (IFLA) website (https://www.ifla.org/publications/node/11174) as a guide, review the following news stories to determine which are real and which are fake. Explain your rationale.

1. Strasbourg market attacker ‘pledged allegiance to ISIS’ – source.

2. Lawmakers in California propose a new law called the “Check Your Oxygen Privilege Act”.

3. Four AI-controlled robots kill 29 scientists in Japan.

4. North Korea says it will not denuclearize until the US eliminates ‘nuclear threat’.

5. Two men found living underneath the Calico Mine Ride at Knott’s Berry Farm.

6. Scientists find a brain circuit that could explain seasonal depression.

7. Amazon customer receives 1,700 audio files of a stranger who used Alexa.

8. NFL fines Pittsburgh Steelers $1M each for skipping National Anthem.

9. FBI raids CDC for data on vaccines and autism.

10. Only 60 of 1,566 churches in Houston opened to help Hurricane Harvey victims.

References:

Anderson, L. W., Krathwohl, D. R., Airasian, P. W., Cruikshank, K. A., Mayer, R. E., Pintrich, P. R., Raths, J., & Wittrock, M.C. (2001). A taxonomy for learning, teaching, and assessing: A revision of Bloom's Taxonomy of Educational Objectives. New York, NY: Pearson, Allyn & Bacon. Bloom, B. (Ed.), Englehart, M., Furst, E., Hill, W., & Krathwohl, D. (1956). Taxonomy of educational objectives, Handbook I: Cognitive domain. New York, NY: McCay. Doyle, A. (2018, October 30). Critical thinking definition, skills, and examples. Retrieved from https://www.thebalancecareers.com/critical-thinking-definition-with-examples-2063745 Figliuolo, M. (2016, August 2). Critical thinking. Retrieved from https://www.lynda.com/Business-Skills-tutorials/Critical-Thinking/424116-2.html Gottfried, J., & Shearer, E. (2016, May 26). News use across social media platforms 2016. Pew Research Center. Retrieved from http://www.journalism.org/2016/05/26/news-use-across-social-media-platforms-2016/ MindValley. (n.d.). How to solve the biggest problems with critical thinking exercises [blog]. Retrieved from https://blog.mindvalley.com/critical-thinking-exercises/# Patel, D. (2018, October 24). 16 characteristics of critical thinkers. Retrieved from https://www.entrepreneur.com/article/321660 TeachThought Staff. (2018, July 29). 6 critical thinking questions for any situation. Retrieved from https://www.teachthought.com/critical-thinking/6-critical-thinking-questions-situation/

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Critical thinking skills in mathematics

Ekasatya Aldila Afriansyah 1 , Tatang Herman 2 , Turmudi 2 and Jarnawi Afgani Dahlan 2

Published under licence by IOP Publishing Ltd Journal of Physics: Conference Series , Volume 1778 , Seminar Nasional Matematika dan Pendidikan Matematika (SEMADIK) 2020 29-30 August 2020, Purwokerto, Indonesia Citation Ekasatya Aldila Afriansyah et al 2021 J. Phys.: Conf. Ser. 1778 012013 DOI 10.1088/1742-6596/1778/1/012013

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1 Institut Pendidikan Indonesia, Jl. Terusan Pahlawan No 83, Sukagalih, Garut 44151, Indonesia

2 Universitas Pendidikan Indonesia, Jl. Dr. Setiabudi No. 229, Sukasari, Bandung 40154, Indonesia

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Teachers' low mathematical critical thinking skills (MCTS) resulted in students' low MCTS in the learning process. A teacher needs to have a good foundation of MCTS so that they can pass on their MCTS to their students. This study aims to improve the teaching and learning activities of teachers through prospective teachers and to find out whether there is an effect of the interaction between learning and Mathematical Prior Knowledge (MPK) of prospective teachers on the achievement of the MCTS. The solution offered in the learning process is Realistic Mathematics Education based on Emergent Modeling (RME-EM). The research method used is quantitative research methods. The research sample is prospective teachers at one of the private universities in West Java, as many as 51 people. The result of the research is that the achievement of the student teaching and learning activities of prospective teachers who get RME-EM learning is better than the achievement of the MCTS of prospective teachers who get conventional learning. On the influence of the interaction between learning (RME-EM and Conventional) and MPK (high, medium, and low) prospective teachers on the achievement of MCTS, it is found that there is an influence on the achievement of student teaching and learning activities based on learning and MPK, but there is no interaction between learning and MPK towards the achievement of prospective teachers. RME-EM learning can be implemented at various student levels and is quite successful in improving teaching and learning activities for prospective teachers. However, RME-EM learning activities are not sufficient to have a significant impact on the interaction between learning and MPK on prospective teachers. RME-EM can be a solution for teachers who want to improve their students' MCTS in the classroom.

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Analysis of mathematical critical thinking skills with visual learning styles in vocational high school

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Nur Sara Sinta Maulida , Sutama; Analysis of mathematical critical thinking skills with visual learning styles in vocational high school. AIP Conf. Proc. 17 January 2024; 2926 (1): 020033. https://doi.org/10.1063/5.0182850

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Critical thinking is used as an assumption in solving problems and can be used to take appropriate provisions. In solving this problem, students use learning styles as a learning method. The purpose of this study is: (1.) Describe students' critical thinking skills on interpretation indicators based on visual learning styles. (2.) Describe students' critical thinking skills on analytical indicators based on visual learning styles. (3.) Describe students' critical thinking skills on evaluation indicators based on visual learning styles. (4.) Describe students' critical thinking skills on inference indicators based on visual learning style. Descriptive qualitative techniques are used in this research. Three students in the visual learner category became the focus of the study. This study used data collection techniques in the form of observation, giving learning style questionnaires to class X AKL 3 students to take research subjects, documents in the form of learning outcomes, and interview documents. The triangulation method ensures the reliability of the data used. Data validity using triangulation techniques. Data analysis techniques used are data reduction, data presentation, and verification. This research resulted in the following:: (1.) The interpretation ability of visual learning style students has an excellent category, which is at a percentage of 91.67%. (2.) The analytical ability of visual learning style students has a good category, which is at a percentage of 75%. (3.) The ability to evaluate students’ visual learning styles has a good category, which is at a percentage of 72.92%. (4.) The inference ability of visual learning style students has a less category, which is at a percentage of 39.58%.

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