There are assessment tools in the site of critical thinking community, but these tools are not free and general. The question is whether there are free tools specifically for mathematical critical thinking. 

you're right !. surely, i'm looking for free ones and especially in math

Best Regards!

Here's a link to a similar question asked regarding CT that contain some links to assessment tools, which I hope will be helpful for you:

https://www.researchgate.net/post/How_can_I_get_the_California_Critical_Thinking_Skill_test_CCTST_in_Bahasa_Malaysia_Where_can_I_purchase_it_Can_anyone_help

I am also including a debating strategy I use in other courses for developing students' critical thinking skills that may give some further insight into your topic:https://www.researchgate.net/publication/274720155_Debating_A_Dynamic_Teaching_Strategy_for_Motivating_Students_and_Teachers

Best regards,

Debra

Conference Paper Debating: A Dynamic Teaching Strategy for Motivating Student...

Thanks a lot for the info

Best Regards!

Hello Otman Jaber

please check the resources

www.criticalthinking.org/pages/critical-thinking-testing-and-assessment/594

https://www.researchgate.net/.../Any_suggestions_in_assessing_critical_thinking_skills

www.niu.edu/assessment/toolkit/vol4_ish4.pd

researchnetwork.pearson.com/wp.../CriticalThinkingAssessmentResearchReport.pdf

https://www.nap.edu/read/2235/chapter/6

cae.org/images/uploads/pdf/The_Case_for_Critical_Thinking_Skills.pdf

www.usma.edu/cfe/literature/goethals_13.pd

Hello Othman Jaber,

Several months ago I also raised similar question. Several answers and suggestions had been given to me. Unfortunately, there was no such mathematical critical thinking test available. If we can work together develop this test, I think it will be great for mathematics education community. 

Hi, I'm also looking for assesment tools for critical thinking but  in environmental education. If anyone can help me. Thanks 

Attached are 2 recent chapters that describe Meaning Equivalence Reusable Learning Objects (MERLO), an assessment tool for critical thinking in mathematics (as well as in other STEM courses). It is part of Pedagogy for Conceptual Thinking that has been shown to enhance learning outcomes.

You may explore the following link for various assessment tools including math:

http://www.assessmentforlearning.edu.au/professional_learning/modules/success_criteria_and_rubrics/success_design_rubrics.html

thank you all for your valuable help

Hi Otman,

It is generally alleged that critical thinking refers to one’s capacity to think clearly and rationally about what to do or what to believe; that it includes one’s ability to engage in reflective and independent thinking; that peoples with critical thinking skills are capable of, for example, understanding the logical connections between ideas, identifying, constructing and evaluating arguments, detecting inconsistencies and common mistakes in reasoning, solving problems in a systematic way, noting the relevance and importance of ideas,  and reflecting on the justification of one's own beliefs and values.

Critical thinking, therefore, is not a matter of compilation of information. A person with a good memory and who knows a lot of facts is not necessarily good at critical thinking. A critical thinker is able to deduce consequences from premises he knows, and he knows how to use information to solve problems, and to seek important sources of information to inform himself/herself.

A common misunderstanding about critical thinking is to judge it as being critical of other people. Although critical thinking skills can be used in exposing logical fallacies and bad reasoning, critical thinking can also play an important role in cooperative reasoning and constructive tasks. Critical thinking, therefore, can help us acquire knowledge, improve our theories, and strengthen arguments. Of course, we can use critical thinking to improve social institutions.

Other common misunderstanding about critical thinking is that it hinders one’s creativity because it requires following the rules of logic and rationality, and creativity might require breaking rules. Critical thinking, however, is quite consistent with thinking, say, "out-of-the-line", challenging consensus and pursuing divergent ideas and less popular approaches. If anything, critical thinking is part and parcel of creativity because we need critical thinking to evaluate and improve our creative ideas.  

The following example clearly illustrates that creativity or divergent thinking and critical thinking are highly consistent with each other. It is said that Karl F. Gauss (1977-1855) left his primary school teacher highly perplex when, at the age of 8 years, he gave a creative answer to the following problem his teacher had written shortly before on the blackboard: “ What is the sum of 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8?”. All of a sudden, and apparently without having time enough to perform the respective operation of adding, Gauss replied that the result of the arithmetical operation at hand was 36. “Why is this so?” -- The teacher asked again. She became more perplex when Gauss replied that this was so because 4 X 9 = 36. “I cannot understand” -- The teacher replied and went on:  “Why did you perform an operation of multiplication instead of an addition operation?”  “I did that -- Gauss replied -- because I easily realized that 1+ 8 = 9; “2 +7 = 9; 3 + 6 = 9; and 4 + 5 = 9. Hence, 4 X 9 = 36”. Even if it were given by a non-expert adult in mathematics, we would certainly say that Gauss’ answer and way of thinking was highly creative and was a clear example of divergent, new, and insightful thinking. As critical thinking also includes one’s ability to engage in reflective and independent thinking, Gauss’ answer is telling example of both creativity and critical thinking in mathematics.

The example also substantiates a procedure of how to get access to one’s critical thinking in mathematics. In other words, to ask individuals to justify their answers or performance on issues wherein critical thinking may be involved is a kind of “think aloud” procedure, a procedure often employed by researchers to get access to underlying psychological processes at issue, for example, in one’s critical thinking and one’s creative thinking or acting.  

Critical thinking often involves evaluating arguments and detecting inconsistencies and common mistakes in reasoning. Because of this the domain of conditional reasoning is an appropriate domain for one to observe individuals’ ability to think critically, that is, to see, for example, how individuals of different ages solve each of four classical logical arguments (i.e., Modus Ponens, Modus Tollens, Denial of Antecedent, and Affirmation of Consequent). Of course, for one to know individual’s critical thinking while solving these logical arguments or problems or other mathematical problems one has to ask them to justify (or think aloud) their responses and solutions.

As you know, conditional reasoning has do to with “if…then statements”.  Modus Ponens: If p (Mary is at school), then q (John is also at school); p is the case (Mary is a school). Hence, q is necessarily the case (John is also at school). Modus Tollens: If p (Mary is at school), then q (John is also at school); not q is the case (John is not a school): Hence, not p is necessarily the case (Mary is not at school). Denial of Antecedent:  If p (Mary is at school), then q (John is also at school); not p is the case (Mary is not at school). Hence, nothing can be concluded about q (i.e., John may be or may be not at school). Affirmation of Consequent: If p (Mary is at school), then q (John is also at school; q is the case (John is at school). Hence, nothing can be concluded about p (Mary may be or may be not at school). There is mounting evidence that shows that even 5-year-olds draw the “correct” conclusion when Modus Ponens is the case (i.e., John is at school), that 9-year-olds draw the “correct” conclusion when Modus Tollens is the case (i.e., Mary it not at school), and that even some adolescents and adults are not capable of drawing the correct conclusion when Affirmation of Consequent and Denial of Antecedent are the case (i.e., It is not possible to say whether or not Mary/John are at school). Of course, children are not capable of dealing with either Affirmation of Consequent or Denial of Antecedent problems. It is worth mentioning, however, that when 9- year-olds or even younger are asked to justify their conclusions when, for example, Modus Tollens is the case, their justifications are not based on critical thinking nor are they based on an idea of logical necessity. More precisely, their justifications for their apparently correct conclusion are based on what is called a matching bias process(i.e., if it is true that If Mary is at school John is also at school, then it is also true that if John is not at school, Mary is not at school either. To be based on an idea of logical necessity and guided by critical thinking, children would have to say that if John not were at school and Mary was there, then it would be necessarily false to say that if Mary is at school John is also at school. It is because of such matching bias that children and even some adolescents and adult say that, in Denial of Antecedent problems, for example, if Mary is not a school, John is not at school either, which amounts to commit a fallacy or draw an incorrect conclusion.  

All that said, critical thinking is a major ability in either theoretical (e.g., to solve conditional reasoning problems) or practical domains (e.g., to critically evaluate our moral decisions and choices in real-real moral dilemmas, such as to steal/not to steal  to save a human life). To ask individuals to think aloud, or justify their answers when they are confronted with issues having to do with critical thinking are but two procedures (not processes) to get access to their critical thinking. Given that in semi-structured interviews, individuals are asked to justify their answers, which, in turn, is a thinking aloud procedure, such interviews are also a good procedure to assess individual’s critical thinking. Needless to say, to ask subjects for justifications, thinking aloud, and performing on semi-structured interviews are deeply intertwined.

I hope I has got your question and that this helps.

Best regards,

Thanks a lot professor Orlando for the interesting detailed analysis.

It is, surely, very important and contributing.

Best Regards

Hi everyone:

there is a very good resource at 

http://schools.cbe.ab.ca/b399/pdfs/Articles%20and%20Documents/WDYDIST_Teaching_EN.pdf

Thank you Lorraine.

Thanks a lot Lorraine!

Hi

You can use California Critical Thinking Skills Test (CCTST) or observation checklist

thank you Rita!.

yes I use math talks with the students.

I'm sure the resources you added are helpful.

Ali,thank you too.I Know The CCTST tool assessment. I'm interested specifically in mathematical CT tool.

Best Regards.