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Critical Thinking

50 Questions Every Student Should Be Able To Answer Before They Graduate High School



50 Questions Every Student Should Be Able To Answer Before They Graduate High School

by Terry Heick

Usually–when it’s discussed at all–the kinds of questions stakeholders in education believe ‘students should be able to answer’ are academic (content-based), or practical (life skills).

Academic questions might include:

How can I use reading strategies to make sense of a text? What is the scientific process? How can I calculate the area of a square or the probability that I’m going to draw a red ball out of this bag versus green? How do governments function?

‘Life skill-based’ questions might include:

How do I apply for a job? How can I create a resume and cover letter that reflects what an employer is looking for? How do I know how much of what medicine I should take, when? How do I open a bank account? How can I create and sustain a balanced budget? What should I do if I feel like I’m being bullied or threatened?

All of these, to varying degrees, are useful questions for students to be able to answer. The key is priority and personalization. What’s most important for that student in that place what that past and that future?

Public education is not designed to even begin answering that kind of question. This is, in part, because education is standardized and built to ‘scale,’ whereas the value of such standardization is limited for most students. So I came up with some questions that, in a perfect world, a student would be able to answer before graduating high school.

A lot of these questions are abstract and open-ended and counter to what is generally taught in schools. And, of course, this is all subjective. Every parent alive would likely come up with a different list (a great start to homeschooling, if that’s your thing).

But after 13+ years and hundreds of thousands of dollars (if not more) invested in that child and their ‘knowledge set,’ it’d be great if they could at least begin to create a credible response that makes sense to them.

50 Questions Every Student Should Be Able To Answer Before They Graduate High School

1. What are people ‘for’? What should a person ‘do’? What is my life philosophy about people and work and knowledge and relationships?

2. Who and ‘where’ am I? Who do I depend on, who depends on me, and how should each inform my values, behaviors, and affections? What are my physical, digital, and emotional interdependencies?

3. What do I know, and what can and should I do with what I know? What are the limits of what I know/my knowledge, and how can those limits inform my behaviors?

4. What do I love? How has that changed over the course of my life so far? What contributes to love and affection? What are its causes and effects? How should love guide my life–and how should it not?

5. What kinds of questions should I be asking on a daily basis—of myself and the people and world around me? Where can I find reliable sources of information to answer my questions?

6. What kinds of conversations should I be having with whom, and how? What does it mean to truly listen to someone, and how should that impact my conversations with them? What are the strengths and weaknesses of certain forms of communication and technology? A conversation versus texting versus a phone call versus a threaded social-media-based debate?

7. When am I at my best? My most creative? Where is my genius? What are the patterns in the kinds of things I tend to be interested in and curious about and is there anything I should ‘take away’ from those patterns? What are my habits, and what are the results of those habits? What are the habits of the person I want to be, and how can I adjust accordingly?

8. What do I ‘believe’? Where do my beliefs come from? How do my beliefs frame and influence what I believe I ‘see,’ and vice-versa? What do I tend to pay attention to and notice on a daily basis? What are the effects of that focus? Should it be refined? How will I know? What are my thinking ‘blind spots’? Cognitive biases, cultural biases, tendencies towards confirmation bias, etc?

9. What’s the difference between a fact and an opinion? Why are they easy to get confused? Why is it important to know the difference?

10. How can I discuss something with someone I disagree with? How can I disagree with someone while learning from them? How can I ‘make a point without making an enemy’? How can I separate a person from an idea? Are there times when that is easier/more difficult?

11. What is the relationship between my thinking, my beliefs, and my behavior (e.g., my work/career, what I read, my priorities, who I hang out with, etc.)?

12. What sorts of thinking and information should go into a decision? Where should I tolerate uncertainty and where should I try to insist on ‘being sure’?

13. What are logical fallacies and thinking traps, and how can and should I avoid them to do better work, have healthier relationships, and create a sense of well-being so that I can define contentment and happiness for myself as I grow older?

14. What influences me, and how can and should I control those influences to my advantage?

15. How do I apologize to someone? How do I know when to do so–and what words and tone and medium to use?

16. What’s possible–for me in my life? What can I dream? Imagine? What should I read, watch, and create? What can I learn from watching others–looking ‘out’? And what can I learn from looking within? How can the two work together?

17. Where do my morals come from? If I have a clear ‘ethical system,’ what is it and what are its influences? And if I don’t, why not? What do I risk/gain by not having one that is at least somewhat defined? What do I risk/gain if I do?

18. What is the difference between learning and education, and how should each serve me in my life?

19. When should I lead and when should I follow? When should I talk and when should I listen?

20. What role can creativity play in my life? Innovation? Disruptive thinking?


21. What are my priorities, and how do my choices and behaviors reflect/not reflect those priorities?

22. How do I define ‘success’? What, if anything, has been holding me back from success (or even more success than I’ve already experienced), and how should I respond?

23. What is the best way to research something? What’s the difference between ‘research’ and ‘Googling’?

24. What is the relationship between a thought, a belief, and behavior? How does one affect one (or both) of the others?

25. How can I decide if something is true or false?

26. What are my goals? How can I categorize those goals? And in light of those goals, what’s the best way to spend the next five years of my life? How have my goals changed over the last five years and why?

27. How can I learn something from everyone I meet?

28. What is the difference between your ‘work,’ a ‘job,’ and a ‘career’? What’s the best way to perform a ‘job search’? How do most people go about this, and how can I do better?

29. How do I respond to challenging situations? How can I reframe my thinking in certain situations, and to what effect?

30. What are my sources of stability, and how can I serve and protect them–and use them to grow?

31. What seems to make me happy? And how do I distinguish between contentment, joy, and happiness?

32. How does timing affect living?

33. Who in my life do I owe what, and why? How should I respond as a result? What am I accountable for? And to whom? What does the world need from me? What do I need from the world?

34. What should I read and why?

35. What role can art, music, and theater play in my life?

36. How can I be more aware of my ‘self’ so that I have a clear and accurate view? What I believe and do? My values? My shortcomings–those I should accept, and those I should work to improve?

37. What lessons can I take from my parents/immediate family as I prepare for ‘the real world’?

38. Who do I consider inspirational/heroic and why? What effect might this have on my ambitions and potential?

39. Where have I succeeded/struggled academically and why? How has this affected me? How should I respond?

40. What’s the problem with the word ‘smart’?

41. What is the relationship between knowledge and critical thinking?

42. How can I understand different ‘situations’ in my life, and how I can use knowledge and critical thinking together to do so?

43. What is the value of another person’s opinion? Does it change depending on what that ‘opinion’ is about–if it’s about me versus a political issue versus how to raise children or buy the ‘right’ house, etc?

44. What are the most important things I’ve learned in school? What can I do with those things that I’ve learned?

45. Which concepts and ideas have I not learned about–or much about–that I should have? What knowledge gaps are most and least important for me in light of who and where I am? And to where and I want to ‘go’?

46. Which skills and competencies come naturally for me, which not so much, and how should I respond?

47. What is a digital footprint and how can I analyze and revise mine to align with who I believe I am and want to be?

48. How can I stay safe–online and offline–by using my ability to think, adapt, and communicate?

49. What is the difference between learning math and science and history versus thinking like a mathematician, scientist, and historian? What can I learn from these differences?

50. What effect do I want to have on the world, and where should I start?

50 Questions Every Student Should Be Able To Answer Before They Graduate High School

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Critical Thinking

35 Psychology-Based Critical Thinking Strategies



35 Psychology-Based Critical Thinking Strategies 

contributed by Sara

Have you ever considered letting your students listen to hardcore punk while they take their mid-term exam?

Decided to do away with PowerPoint presentations during your lectures? Urged your students to memorize more in order to remember more?

If the answer is no, you may want to rethink your notions of psychology and its place in the learning environment. In pursuit, here are 35 psychology-based critical thinking strategies for use in your classroom.

35 Psychology-Based Critical Thinking Strategies

1. State-Dependent Recall

Definition: It is easiest to recall information when you are in a state similar to the one in which you initially learned the material.

Application: Urge your students to sit in the same room they studied in when they complete their take-home quiz. Let them listen to music when they complete their mid-term essays if they usually listen to it when they write.

2. The Fundamental Attribution Error

Definition: This cognitive bias is specifically the tendency to overemphasize internal explanations for the behavior of others while failing to take into account the power of the situation. The student who says, “Brian got an A on his English paper because he is smarter than I am” instead of “Brian got an A on his English because he visited the Writing Center before he turned it in” suffers from the Fundamental Attribution Error.

Application: Sometimes students need your help distinguishing between internal and external factors that affect academic performance.

3. Effort Justification/Change Bias

Definition: After an investment of effort in producing change, remembering one’s past performance as more difficult than it actually was, thereby inflating the perceived value of the result.

Application: Unfortunately, effort does not always correlate positively with performance. Students may be angry if they do not receive the grade they expect on an assignment that cost them a lot of time. In your comments, always mention the work you see even if it misses the mark.

4. Cognitive Dissonance

Definition: Cognitive Dissonance is the feeling of psychological discomfort produced by the combined presence of two thoughts that do not follow from one another, often resulting in the adoption of beliefs that align with one’s actions but contradict the beliefs one held before the action was committed.

Application: F. Scott Fitzgerald once said, “The test of a first-rate intelligence is the ability to hold two opposed ideas in the mind at the same time, and still retain the ability to function.” The world isn’t black or white, and neither is the mind. Share this wisdom with your students to promote critical thinking.

5. Chunking

Definition: A term referring to the process of taking individual units of information (chunks) and grouping them into larger units. Probably the most common example of chunking occurs in phone numbers. For example, a phone number sequence of 4-7-1-1-3-2-4 would be chunked into 471-1324. Chunking is often a useful tool when memorizing large amounts of information. By separating disparate individual elements into larger blocks, information becomes easier to retain and recall.

Application: A great tool for students who must memorize long series of names, numbers, pictures, dates, terms, etc.

6. Positive Reinforcement

Definition: Positive reinforcement is a concept first described by psychologist B. F. Skinner in his theory of operant conditioning. Positive reinforcement is anything added that follows a behavior that makes it more likely that the behavior will occur again in the future. One of the easiest ways to remember this is to think of something being added to the situation.

Application: Bonus and extra credit assignments are some of the most basic examples of positive reinforcement. More nuanced techniques might include positive verbal feedback, class celebrations (but not reward competitions), or opportunities to contribute individually to the curriculum.

7. Spaced Repetition

Definition: A learning technique that incorporates increasing intervals of time between subsequent review of previously learned material in order to enhance retention. Proven to be significantly more effective than massed repetition (i.e. cramming).

Application: One of the most valuable things you can do to help students retain information is to hold weekly review sessions. Go over not only the main concepts presented in the past five days, but also touch on concepts covered multiple weeks or months ago.

8. Multi-Modal Learning

Definition: The more ways in which you learn something (visually, aurally, kinesthetically, verbally, etc.), the better you remember it. A key advantage of interdisciplinary courses and programs.

Application: Provide examples of major concepts in different modes. Use texts, videos, recordings, visual representations, and creative exercises to reinforce the material.

9. Declarative Knowledge vs. Procedural Knowledge

Definition: Knowing “what” (facts) as opposed to knowing “how” (procedural knowledge).

Application: It is downright difficult, if not impossible, to train complex cognitive skills in a single semester; yet look what most problem solving courses in the corporate training world are—a couple of hours, eight hours tops.

We expect learners to transfer what they have learned in the classroom to the job, but all they have are a very few simple if/then statements to take back to the job. Keep in mind that teaching your students “what” is not the same as teaching them “how.”

10. The Method of Loci

Definition: A mnemonic device used in ancient Greek and Roman times wherein items to be remembered are mentally associated with specific physical locations. Examples include the various rooms of a house and paths through the forest.

Application: A great tool to help students memorize terms, related concepts, or anything else that can be “placed” as an image on a mental map.

11. Interacting Images

Definition: An item is much more likely to be remembered if it is imagined as being actively involved with another item in some way rather than sitting there doing nothing. When items are intertwined or associated they are said to be interacting and they become a single chunk or whole in memory.

Application: It is far more difficult to remember concepts and definitions than it is to remember actions and descriptions. So, use the latter to trigger the former. If you are teaching your law students about double jeopardy, advise them to imagine someone robbing a bank, going to jail, then robbing the same bank again, free of conviction.

12. Dual Coding

Definition: The ability to code a stimulus two different ways increases the chance of remembering that item compared to if the stimulus was only coded one way. For example, say a person has stored the stimulus concept, “dog” as both the word ‘dog’ and as the image of a dog. When asked to recall the stimulus, the person can retrieve either the word or the image individually or both, simultaneously. If the word is recalled, the image of the dog is not lost and can still be retrieved at a later point in time.

Application: Never present students with lists of keywords and definitions without adding stimuli (or letting them add their own). They will be far more likely to recall the difference between sedimentary and igneous rocks if they associate the former with baking a layer cake and the latter with crystallizing caramel. Trust me – adding images reduces the effort needed to remember.

13. The Immediate Environment

Definition: Multiple studies have shown a dependence on context of one’s environment as an aid to recall specific items and events.

Application: Simply remembering what you were wearing when you learned the 1st amendment of the Constitution will help you recall the material later. Encourage students to use their immediate learning environment to build associations and boost memory.

14. Dichotic Listening Task

Definition: A useful way to study selective attention, this test involves different auditory stimuli presented directed into different ears over headphones. Participants are instructed to repeat aloud the words they hear in one ear while a different message is presented in the other ear.

People do not recall the attended message well, and are generally able to report almost nothing about the content of the unattended message. In fact, a change from English to German goes unnoticed. Some things, however, such as the participant’s name being spoken (called ‘the cocktail effect’) and a switch from the voice of one gender to another, are noticed.

Application: It is not every day that students are asked to listen to two different streams of voice recordings at once, but they are asked regularly to process multiple messages at once—often to their own disadvantage. Requiring students to copy notes written on an overhead while you lecture, for instance, is a ridiculous habit that should have been phased out long ago. How can any teacher reasonably expect this to be effective?

15. Change Blindness

Definition: A psychological lack of attention unassociated with any defects or deficits. One famous Harvard study asked subjects to watch a short video of two groups of people (wearing black and white t-shirts) pass a basketball around. The subjects are told to either count the number of passes made by one of the teams or to keep count of bounce passes vs. aerial passes.

In different versions of the video, a woman walks through the scene carrying an umbrella or wearing a full gorilla suit. After watching the video the subjects are asked if they saw anything out of the ordinary take place. In most groups, 50% of the subjects did not report seeing the gorilla. The failure to perceive the change is attributed to the failure to attend to it while engaged in the difficult task of counting the number of passes of the ball.

Application: Unfortunately, human attention is not designed to absorb important facts just because they are important. When you are highlighting important definitions or differences between concepts—things that require considerable attention—don’t require your students to be doing anything else but listening to you speak. Otherwise, that “gorilla” you deem so pivotal in World War I will walk on by unnoticed, so to speak.

On the other hand, if you are reviewing familiar materials, multi-tasking is acceptable, since students have already captured the material at least partially in their long-term memory store.

16. Bottom-up & Top-down Processing

Definition: Strategies of information processing and knowledge ordering. The top-down approach, also known as deductive reasoning, involves starting with the bigger picture and breaking it down into smaller segments in order to derive a theory. The bottom-up approach, also known as inductive reasoning, involves beginning with a small segment of information and growing into a more complex, bigger picture. The former uses known data first to form a perception; the latter uses incoming data from the environment first to form a perception.

Application: Be aware of the type of processing you are expecting when you assign a project or ask a question. Different fields require different types of processing: top-down is more prevalent in the sciences and bottom-up is more prevalent in the humanities. Try to phrase questions in terms of big picture first, small picture second or small picture first, big picture second.

17. Divided Attention

Definition: Divided attention concerns our ability to ‘multitask’, i.e. whether we can attend to more than one task at a time. While the dichotic listening task involves trying to attend to only one message, in studies of divided attention the task is to attend to more than one source of information. Early studies have shown two important factors that determine our ability to multitask: 1) The similarity of the tasks. Allport et al. (1972) asked participants to learn a set of words while shadowing a spoken message. They found that the words could be learned when they were presented visually but not when they were presented as spoken words.


However, if messages were sufficiently different then both could be attended to. 2) How well practiced we are at the task. Spelke et al. (1976) found that, with practice, students could learn to read a story while writing down a list of words read out loud to them.

Application: Students should not be expected to arrive to class with well-honed multi-tasking skills, especially after a long vacation or break from studies. It’s best for instructors to ease students into tasks that involve divided attention.

18. Serial vs. Parallel Processing

Definition: Learning one object at a time, sequentially (serial processing), versus learning all of them at once (parallel processing).

Application: Cognitive psychology compares the processing of the human mind to the information processing of computers. Computers operate largely under a serial processing system, and the human mind has been shown to function more efficiently this way as well.

19. Incidental Memory

Definition: Information acquired without intention, often just as memorable as information acquired with intention. Craik and Tulving demonstrated that it was not the intention to learn that was critical for later memory, but rather the type of processing engaged at the time of encoding. Information that was processed meaningfully was well remembered whether or not there was an intention to retain it.

Application: This is solid evidence that asking your students to ‘study hard’ simply isn’t enough. You will have to present the information in a memorable way (using emotion, personalization, or any number of the tips listed here) or urge students to adopt effective memorization strategies.

20. Working Memory Capacity

Definition: Working (or short term) memory is generally considered to have a limit of about 7 elements, or chunks.

Application: Design your lesson plans around this number, and don’t expect your students to effectively process more terms or concepts than this in a given session.

21. Priming

Definition: An effect in which exposure to a stimulus influences a response to a later stimulus. For example, if a person reads a list of words including the word table, and is later asked to complete a word starting with tab, the probability that he or she will answer table is greater than if they had not been primed.

Application: Larry Ferlazzo uses priming with his students before tests, asking them to spend a few minutes writing on a topic covered in the quiz.

22. Schema

Definition: A way of organizing current knowledge that provides a framework for future understanding. Examples of schemata include academic rubrics, social schemas, stereotypes, social roles, world views, and archetypes. The brain automatically uses schema to process and understand new information more efficiently.

Application: The brain doesn’t remember facts; it remembers connections. In English and literature instruction, for example, urge students to make connections between the text at hand and their own lives, the text at hand and other texts they’ve read, and the text and the world around them.

23. Forgetting Curve

Definition: A graph that hypothesizes how information is lost over time when there is no attempt to retain it. A typical curve shows that humans tend to halve their memory of newly learned knowledge in a matter of days or weeks unless they consciously review the learned material.

Application: More cognitive evidence for spaced repetition and weekly reviews of learned material. Forgetting happens fast—don’t just review before the test!

24. Episodic vs. Semantic Memory

Definition: Episodic memory is recall for events (or episodes) that happened in the past; semantic memory is recall for specific facts. These two types of memory occur in different parts of the brain.

Application: Many people assume that recalling the name of the 13th president should be as easy as recalling how you learned to ride a bicycle. On the contrary, these types of memory operate very differently in the brain, and recalling anything that has personal value is much easier than recalling a random fact. Using episodic memory to enhance semantic memory can be a useful tool—much like interacting images and dual coding.

25. Social-Emotional Learning (SEL)

Definition: Psychologists in the 1980s found that attributes like self-restraint, persistence and self-awareness might actually be better predictors of a person’s life trajectory than standard academic measures. Now a movement is in the works across school districts to promote “emotional literacy” in students.

Application: Allow students to sort through their feelings about your class or subject with assignments that call for self-reflection. Although this technique is mostly geared towards children whose emotions are not yet fully developed, emotion affects learning at any age.

26. Metacognition

Definition: Cognitive psychologists use the term metacognition to describe our ability to assess our own skills, knowledge, or learning. That ability affects how well and how long students study—which, of course, affects how much and how deeply they learn. Students with poor metacognition skills will often shorten their study time prematurely, critical thinking that they have mastered course material that they barely know.

Application: Studies show that awareness of one’s learning is enough to enhance it. Help students step back and assess their own habits and skills.

27. Knowledge Organization

Definition: The hierarchical method of organizing information and how it maps well onto the brain’s memory.

Application: One well-known example of knowledge organization is instructional scaffolding, wherein guidance is provided to novices until they begin to master the material, at which point the ‘scaffolding’ is removed. This process compliments the hierarchical nature of learning.

28. Pattern Recognition

Definition: Pattern recognition refers to the process of recognizing a set of stimuli arranged in a certain pattern that is characteristic of that set of stimuli. It does not occur instantly, although it does happen automatically and spontaneously. Pattern recognition is an innate ability of animals.

Application: Some types of recognition, such as facial recognition and pattern recognition, require large amounts of brain processing capacity. This is why the ability to make connections (or recognize patterns) has been linked time and time again to intelligence. The main systems our brains use to organize information (schemas, heuristics, etc.) rely on patterns. Point out patterns to your students as often as possible to promote critical thinking skills and heightened comprehension.

29. Anchoring

Definition: The common human tendency to rely too heavily on the first piece of information offered (the “anchor”) when making decisions. For example, the initial price offered for a used car sets the standard for the rest of the negotiations, so that prices lower than the initial price seem more reasonable even if they are still higher than what the car is really worth.

Application: To prevent this, promote delayed gratification and teach your students that the first reasonable answer presented is not always the right answer.

30. Choice-Supportive Bias

Definition: Remembering chosen options as having been better than rejected options.

Application: There is nothing wrong with changing your mind in light of new evidence. Students’ reasons for liking or disliking subjects are often based on experiences they can hardly remember or explain. Urge students to be open to new attitudes and critical of old ones.

31. Context Effect

Definition: The idea that cognition and memory are dependent on context, such that out-of-context memories are more difficult to retrieve than in-context memories (e.g. recall time and accuracy for a work-related memory will be lower at home, and vice versa).

Application: A close relative of state-dependent learning and priming. Providing the right context for a question or concept can make all the difference—more difference even than wording, tone of voice, or student mastery.

32. Primacy & Recency Effect

Definition: The finding that memory recall is higher for the first item(s) on a list and the last item(s) on a list.

Application: Present important concepts at the beginning of a lesson and at the end. Much of what’s in the middle will likely be lost, so you don’t want to deliver the main material you plan to test your students on then.

33. Verbatim Effect

Definition: That the ‘gist’ of what someone has said is better remembered than the verbatim wording.

Application: Expecting students to remember the verbatim wording of an answer is asking too much in most cases. On the other hand, asking students to re-phrase important statements, events, or concepts in their own words greatly enhances the likelihood that they will recall the gist of what they need to learn.

34. Tip-of-the-Tongue phenomenon

Definition: When a subject is able to recall parts of an item, or related information, but is frustratingly unable to recall the whole item. This is thought to be an instance of ‘blocking’ where multiple similar memories are being recalled and interfere with each other.

Application: An extremely common phenomenon in any testing environment. ‘Blocking’ can be reduced with many of the tricks mentioned above, including context, dual coding, chunking, and interacting images. Remember that all a student needs to recall a fact is the correct ‘retrieval cue.’

35. Heuristics

Definition: A heuristic is an experience-based technique that helps in problem solving, learning, and discovery. A heuristic method is particularly used to rapidly come to a solution that is hoped to be close to the best possible answer, or ‘optimal solution.’ Heuristics are ‘rules of thumb,’ educated guesses, intuitive judgments, or simply common sense. An example is the availability heuristic, a mental shortcut that occurs when people make judgments about the probability of events by the ease with which examples come to mind.

Application: As Doug Belshaw of Mozilla writes on his blog, “It can actually be damaging to 1) launch into using educational technologies without thinking them through properly (the how and not just the what); and 2) attempt to replicate what someone else has done elsewhere without thinking about the context.”

Look before you leap, even if the leap seems quick and effective.

35 Psychology-Based Critical Thinking Strategies; This post first appeared on; image attribution flickr user tulanepublicrelations

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Critical Thinking

The 4 Cs: A Framework For Improving Math Skills



The 4 Cs: A Framework For Improving Math Skills

contributed by Anastasia Betts, VP Curriculum Planning and Design at Age of Learning

The U.S. is lagging behind in math literacy.

According to the Program for International Student Assessment (PISA), American teens are well below standard proficiency. However, the breakdown in math literacy is occurring during early childhood, well before the teen years.

Research has shown that early development of math skills and knowledge is a strong predictor of later math achievement. According to recent data from the creators of ABCmouse, Age of Learning, nearly 70% of parents are incorrectly assuming their child is spending the necessary amount of time they need, in and out of school, engaged in math-based learning to be proficient. Moreover, most homes spend time focusing on helping very young children learn to read and write their numerals, while other types of math activities may provide more benefit.

The key to improving the home math environment for young children is to move beyond simple counting exercises. The ‘Four Cs’ is a strategy designed to help parents remember the different kinds of activities that are most useful to young children when learning about math.

The Four Cs stand for Converse, Count, Compare, Categorize, each of which are critical to the development of a young child’s mathematical knowledge. This strategy can improve the quality of parent-child math discussions, and through targeted conversation, help children develop the vocabulary needed for a solid mathematics foundation.


Talking to children about numerical concepts is crucial, as it helps to build not only their math vocabulary but also their knowledge of and curiosity about math concepts.

Conversations should be centered around everyday activities that relate to the child’s lived experiences (e.g., skipping rope, taking a walk in the park, doing activities around the house), as children are likely to be more engaged and connect more with these activities rather than more formal activities (e.g., workbooks, etc.).

Use questions to drive the conversation and encourage your child’s use of strategies for critical thinking. It’s relatively easy for parents to introduce math conversations into daily activities with their children. Asking how many, which has more or less, which is taller, shorter, or bigger, which items ‘go together’ or belong in the same group, are all great conversation starters. Perhaps most importantly, parents should ask children why they think something is true, or how can you show that this is true?

For example, when comparing different groups of items, parents can ask how do you know this group has more than that group? How can you show that your idea is true?



Research continues to show that a wide variety of counting experiences are vital to the development of children’s strong number sense. Counting means more than just saying the number sequence, as it can refer to reciting the count sequence, counting the total number of objects in a pile, counting out a certain number of items from a pile, or counting on a few more to an existing group of items. It can also mean counting forward and backward from a given number.

It’s important for parents and caregivers to develop an awareness of the different types of counting experiences they can share with their children, and look for opportunities to do more than just recite or recognize numbers (e.g., counting apples to buy from the grocery store, sharing out 10 grapes each for lunch, etc.).


Comparing is an important skill that underpins much of mathematics and other sciences as well. Helping young children realize that there are many attributes that can be observed and compared helps prepare them for more sophisticated math concepts that will come later. Parents should invite children to think about the characteristics that different objects possess, such as color, shape, position, and more (e.g., this one is darker blue, this one is lighter blue; this one has more, this one has less; this one has four sides, that one has only three).

Quantity is also an attribute that children must come to understand and recognize, as it is a critical milestone in a young child’s mathematical foundation (e.g., who has more grapes? You or me? How do you know? Etc.).

One way to build and strengthen a child’s ability to compare is through the use of puzzles. Puzzles provide ideal opportunities to help children think critically about comparisons; as the child examines the puzzle pieces to see where they should be placed, children observe color, pattern, and shape. These early observations and comparisons prepare children for the critical thinking they will do later on in math and science.


There are many opportunities in everyday activities for children to categorize and sort. Children are capable of organizing a bookshelf according to shape and size, organizing the pantry by food type, helping fold the laundry and sorting by clothing type, loading or unloading the dishwasher or dish rack, etc. Understanding the characteristics that make something belong (or not belong) to a group is an important part of their mathematical foundation (e.g., all of these shapes are rectangular, and all of these shapes are triangular, etc.).

There are so many rich mathematical experiences that parents and children can have together. The Four Cs provides a simple way to help build parent awareness of these kinds of activities. Using the Four Cs, parents can incorporate daily math experiences that move beyond simple rote counting to the more advanced early math experiences that lead to success in school mathematics and beyond.

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Critical Thinking

15 Questions Students Can Ask Themselves When Learning New Content



15 Questions To Ask When Introducing New Content To Students

by Terry Heick

It just might be that in a society where information is abundant, thinking habits are more important than knowledge.

Somewhere beneath wisdom and above the ‘things’ a student knows. Laws of economics say that scarcity increases value. It’s no longer information that’s scarce, but rather meaningful response to that information. 


And thought has a source–a complex set of processes, background knowledge, and schema that we can, as educators think of as cognitive habits. And if they’re habits, well, that means they’re probably something we can practice at, doesn’t it?

The Navigation Of Information

Even in the age of information, not every student has a smartphone; not every classroom has WiFi; not every home has tablets, or even dictionaries, magazines, and other “packaged data.”

We’ve talked about how teaching might adjust to the Google generation. To claim that the advent of Google makes knowledge–knowing–irrelevant is silly. The ubiquity of information can’t dissolve its value. It doesn’t stop being useful or changing or compelling because there’s a lot of it and its more accessible than at any time in human history.

But it does move knowledge around a bit on the bustling concept map of understanding–changes it in priority, and gives us a chance to see the learning process in a different way.

Instead of a teacher distributing information for students to absorb, many (most?) students can now access that information directly. This suggests, among other revelations, that the navigation of that knowledge is, to the student, more immediately useful than the knowledge itself. And that navigation, rather than being about strategies, is most immediately about habits. How do students respond when confronted with new ideas? Data, systems, patterns, concepts, and just maybe some degree of cognitive dissonance.

What does their mind literally do at that moment they see something new? That moment, like the inception of the universe itself, is what we need to slow down and try to understand. Neurology can help, but we can see it with our own eyes in the classroom. What do they do? What do you notice? And what have you done to create that response?

Questions To Ask As Metacognitive Practice

Metacognition isn’t a matter of a ‘lesson,’ or a teacher telling students it’s something they should do. Rather, it’s a matter of habit. Habits are everything. So, below are 15 questions to help students respond to new ideas, and begin to establish the kinds of habits that make thinkers, and just maybe, starting telling you what you want to hear.

Whether or not they truly become habits depends on how you use them. If you make them useful and familiar and meaningful, or alien, adult-sounding, and awkward. That’s on you as a teacher of your grade level and content area and school and community.

You might notice, though, the student-centered and purposefully-uncertain language used. Might. Suggest. Me. I. Could. Naturally. What stands out to me?

If you say, “What stands out?”, there’s an implication that there is something you’ve already noticed, as a teacher, and you want to know if they see it too. And if they do see it, they’re smart, and if not, they can continue to guess what you’re thinking. This not only decenters the student but the content as well, devolving the process into a distracting game of cat and mouse.

By saying “What stands out to you?”, you’re asking the student to internalize this ‘new idea’–a right angle, verbal irony, the speed of light, etc.–to stop short of ‘understanding’ and simply observe. Approach it carefully and playfully.

What do you see?

That’s it. When they have trouble responding even here, you’ll know that it’s not knowledge that’s the problem, but rather confidence, self-efficacy, and the thinking habits they fall back on when ‘put on the spot’ by a teacher.


One of the most powerful ways to learn is practice. Giving students the opportunity to learn not information, but reflective and reflexive habits that help create learners. Thinkers. Students not only capable of thinking for themselves but prone to do so as a matter of habit.

As a teacher, on a daily basis you’re exposing students to new ideas–or existing ideas in new ways. How are you supporting them in these cognitive disruptive events? How are you teaching them to think?

15 Questions To Ask When Introducing New Content To Students

1. Which parts of this are new to me, and which parts do I recognize?

2. How does this connect with what I already know? How and where does it ’fit’?

3. What stands out to me?

4. Is this subjective or objective?

5. If subjective, is it my judgment necessary for understanding?

6. What does this remind me of?

7. Is this idea important to me? To others? Why or why not?

8. What could I do or make with this?

9. How might others use information like this in the ‘real world’?

10. What real-world models–examples–relate to this that can help me understand this further?

11. What follow-up questions does this suggest I ask?

12. What person, group, or community does this suggest that I connect with?

13. Is there a ‘part’ of this new idea I can take and ‘pivot’? Create something new and fresh?

14. What’s most interesting to me, as a thinker?

15. Where can this learning take me?

15 Questions To Ask That Can Help Student Make Sense Of New Ideas

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