Giải quyết vấn đề sáng tạo (Creative Problem Solving)


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Problem solving là gì? 6 bước giải quyết vấn đề theo chuẩn PMI
Tìm hiểu những kỹ thuật và chiến lược giải quyết vấn đề (problem solving) có thể giúp bạn xử lý hiệu quả những thách thức bạn gặp phải trong các dự án của mình.
Giải quyết vấn đề (problem solving) là gì?
Giải quyết vấn đề đòi hỏi phải tìm giải pháp cho các vấn đề, sự cố hoặc thách thức. Nó có thể bao gồm thu thập thông tin bổ sung, tư duy phê phán (critical thinking), phương pháp tiếp cận sáng tạo, định lượng và/hoặc logic.
Giải quyết vấn đề hiệu quả và có hệ thống là một yếu tố cơ bản trong đảm bảo chất lượng (quality assurance) và cải tiến chất lượng. Các vấn đề có thể phát sinh do kết quả của quy trình Kiểm soát chất lượng (Control Quality) hoặc từ kiểm toán chất lượng (quality audit) và có thể được liên kết với một quy trình hoặc giao phẩm . Sử dụng một phương pháp giải quyết vấn đề một cách cấu trúc sẽ giúp loại bỏ vấn đề và phát triển một giải pháp lâu dài.
Một số vấn đề có thể là nhỏ và có thể được giải quyết nhanh chóng. Các vấn đề khác là lớn và có thể đòi hỏi thời gian và nỗ lực đáng kể để giải quyết. Cho dù vấn đề bạn đang tập trung xử lý là nhỏ hay lớn thì sử dụng cách tiếp cận có hệ thống để giải quyết nó sẽ giúp bạn trở thành giám đốc dự án hiệu quả hơn. Có 6 bước giải quyết vấn đề theo chuẩn PMI:
- Xác định vấn đề
- Xác định nguyên nhân gốc rễ
- Tạo ra các giải pháp khả thi
- Lựa chọn giải pháp tốt nhất
- Thực hiện giải pháp
- Xác minh hiệu quả giải pháp
Sáu bước giải quyết vấn đề theo chuẩn PMI
1. xác định vấn đề.
Điều quan trọng nhất của các bước giải quyết vấn đề là xác định chính xác vấn đề. Cách bạn xác định vấn đề sẽ xác định cách bạn cố gắng giải quyết nó. Ví dụ: nếu bạn nhận được khiếu nại từ khách hàng về một trong các thành viên nhóm dự án của bạn, các giải pháp bạn đưa ra sẽ khác nhau dựa trên cách bạn xác định vấn đề. Nếu bạn xác định vấn đề là do hiệu suất kém của thành viên nhóm dự án thì bạn sẽ phát triển các giải pháp khác so với vấn đề là do kém trong việc xác định mong đợi của khách hàng.
2. Xác định nguyên nhân gốc rễ
Khi bạn đã xác định được vấn đề, bạn sẵn sàng đào sâu hơn và bắt đầu xác định nguyên nhân gốc rễ gây ra sự cố. Bạn có thể sử dụng biểu đồ xương cá (fishbone diagram, còn có các tên gọi khác như cause-and-effect diagram, why-why diagram, Ishikawa diagram) để giúp bạn thực hiện phân tích nguyên nhân và kết quả. Nếu bạn coi vấn đề là một khoảng cách giữa nơi bạn đang ở và nơi bạn muốn, thì nguyên nhân của vấn đề là những trở ngại ngăn cản bạn thu hẹp khoảng cách đó ngay lập tức. Mức phân tích này rất quan trọng để đảm bảo các giải pháp của bạn giải quyết các nguyên nhân thực sự (nguyên nhân gốc rễ) của vấn đề thay vì các triệu chứng của vấn đề. Nếu giải pháp của bạn khắc phục một triệu chứng thay vì nguyên nhân thực tế, thì vấn đề có thể sẽ tái diễn do nó chưa bao giờ thực sự được giải quyết.

Biểu đồ xương cá
3. Tạo ra các giải pháp khả thi
Một khi công việc khó khăn trong việc xác định vấn đề và xác định nguyên nhân của nó đã được hoàn thành, đã đến lúc sáng tạo và phát triển các giải pháp khả thi cho vấn đề. Hai phương pháp giải quyết vấn đề tuyệt vời mà bạn có thể sử dụng để đưa ra giải pháp là động não (brainstorming) và lập bản đồ tư duy (mind mapping).
4. Lựa chọn giải pháp tốt nhất
Sau khi bạn đưa ra một số ý tưởng có thể giải quyết vấn đề, một kỹ thuật giải quyết vấn đề bạn có thể sử dụng để quyết định xem cái nào là giải pháp tốt nhất cho vấn đề của bạn là phân tích đánh đổi (trade-off analysis) đơn giản. Để thực hiện phân tích đánh đổi, hãy xác định các tiêu chí quan trọng cho vấn đề mà bạn có thể sử dụng để đánh giá mỗi giải pháp. Việc đánh giá có thể được thực hiện bằng cách sử dụng một ma trận đơn giản. Giải pháp xếp hạng cao nhất sẽ là giải pháp tốt nhất của bạn cho vấn đề đó.
5. Thực hiện giải pháp
Khi bạn đã xác định giải pháp nào bạn sẽ thực hiện, đã đến lúc hành động. Nếu giải pháp liên quan đến một số hành động hoặc yêu cầu hành động từ người khác, thì nên tạo một kế hoạch hành động và coi nó như một dự án nhỏ.
6. Xác minh hiệu quả giải pháp
Dữ liệu và kết quả thu thập được từ giai đoạn thực hiện giải pháp sẽ được đánh giá. Dữ liệu được so sánh với các kết quả dự kiến để thấy bất kỳ sự tương đồng và khác biệt, từ đó xác minh được hiệu quả của giải pháp.
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Problem Solving – “Vũ khí” chinh phục nhà tuyển dụng khó tính

Tomorrow Marketers – Trong cuộc khảo sát của World Economic Forum , báo cáo đã xếp hạng 10 kỹ năng mà lực lượng lao động cần có để trở nên nổi bật tại nơi làm việc như: tư duy phản biện, sáng tạo, trí tuệ cảm xúc,… Nhưng đứng đầu bảng xếp hạng này lại chính là kỹ năng giải quyết vấn đề (Problem Solving). Vậy cụ thể problem solving là gì và tại sao kỹ năng này lại được nhà lãnh đạo của các doanh nghiệp lớn coi trọng như vậy? Hãy cùng Tomorrow Marketers tìm hiểu qua bài viết dưới đây nhé!
Problem Solving là gì?
Problem Solving (Kỹ năng giải quyết vấn đề) là việc sử dụng tư duy logic, trí tưởng tượng để “hiểu” vấn đề là gì, từ đó đưa ra giải pháp tối ưu trong một tình huống. Nó liên quan đến việc xác định vấn đề, đưa ra các giải pháp, đánh giá, lựa chọn và hành động. Nhà tuyển dụng sẽ quan tâm đến cách bạn tiếp cận và giải quyết các vấn đề phát sinh tại nơi làm việc. Vì vậy, khả năng giải quyết vấn đề là một trong những tiêu chí chính của các nhà tuyển dụng. Họ dựa vào đó để đánh giá khả năng tư duy, sáng tạo, phân tích, giao tiếp và đưa ra quyết định của ứng viên.
Tầm quan trọng của Problem Solving
Người được trang bị kỹ năng giải quyết vấn đề tốt sẽ xử lý những rủi ro phát sinh một cách nhanh chóng, chủ động. Hơn nữa, họ không sợ những điều chưa biết và không ngại khó khăn trong công việc. Đây chính là phẩm chất mà nhà tuyển dụng luôn tìm kiếm ở một ứng viên tiềm năng. Một số lợi ích mà kỹ năng giải quyết vấn đề đem lại:
- Quản lý thời gian tốt, tập trung vào những điều quan trọng
- Lập kế hoạch, sắp xếp công việc và thực thi chiến lược
- Khả năng sáng tạo, nhìn thấy được cơ hội ngay trong khó khăn
- Làm việc dưới áp lực cao
- Xử lý rủi ro
Bằng cách nào nhà tuyển dụng kiểm tra kỹ năng Problem Solving của ứng viên?
1. đặt câu hỏi về kinh nghiệm quá khứ.
Một trong những cách phổ biến nhất là thông qua câu hỏi về hướng giải quyết vấn đề trong quá khứ. Khi phỏng vấn, bạn sẽ thường xuyên gặp những câu hỏi như:
- “Hãy kể về một tình huống khó khăn mà bạn đã đối mặt trong quá khứ”,
Ứng viên nên đưa ra 1 – 2 tình huống mà bạn đã thực sự giải quyết vấn đề tốt. Các nhà tuyển dụng sẽ dựa vào câu trả lời của bạn để hiểu tích cách, cá tính của bạn. Hơn nữa, cách bạn sẽ giải quyết các vấn đề khác trong tương lai với tư cách là nhân viên sẽ được thể hiện. Nhà tuyển dụng cũng sẽ đặt các câu hỏi đào sâu từ câu trả lời của ứng viên. Bạn tuyệt đối không nên “nói quá” hoặc “bịa” ra tình huống mà bạn không thật sự làm nhé.
Bạn có thể tham khảo phương pháp “STAR” để làm nổi bật khả năng giải quyết vấn đề của mình:
S – Situation: Tình huống
T – Task: Nhiệm vụ
A – Action: Hành động
R – Result: Kết quả
Ví dụ, đối với câu hỏi “Hãy kể về tình huống bạn gặp một vấn đề nghiêm trọng cần giải quyết và cách bạn giải quyết vấn đề đó”, bạn có thể áp dụng mô hình STAR như sau:
Trong năm ba đại học, em được bầu làm Phó chủ tịch. Em phụ trách các chương trình của hội sinh viên tại trường đại học. Các nhiệm vụ của vị trí này là tìm kiếm các diễn giả chất lượng, phù hợp cho các hội thảo, workshop, truyền thông chương trình tới cộng đồng sinh viên trường. Và sau đó em cần đánh giá chất lượng sau chương trình.
Số lượng sinh viên tham dự các hội thảo, workshop và cuộc thi đã giảm đáng kể so với năm trước. Nhiệm vụ của em là thực hiện các chương trình để giải quyết vấn đề này. Từ đó, số lượng người tham dự sẽ tăng lên 25% so mốc năm ngoái.
Em đã đề xuất thành lập 1 team làm cuộc khảo sát xác định sở thích của sinh viên để tìm kiếm nguyên nhân của vấn đề. Chúng em lựa chọn ngẫu nhiên các bạn sinh viên cho một cuộc phỏng vấn nhóm tập trung. Em đã học về kỹ thuật nghiên cứu này trong lớp học Marketing của mình và nghĩ rằng nó sẽ giúp xác định lý do tại sao lượng người tham dự lại giảm. Chúng em đã tìm ra vấn đề chính thông qua kết quả khảo sát. Các bạn sinh viên cho rằng thời lượng của các buổi quá dài. Hơn nữa, những kiến thức tại các buổi workshop quá khó để áp dụng vào thực tế.
Nhờ thế mà nhóm đã xây dựng những tiêu chí cụ thể trong việc lựa chọn diễn giả. Các diễn giả cũng được yêu cầu phải có các kịch bản cụ thể tại các buổi workshop. Chúng em sau đó đã chọn các diễn giả cho cả năm cho các sự kiện thường niên. Sau đó, chúng em tạo ra ấn phẩm quảng cáo mô tả từng chương trình và diễn giả nổi bật. Dưới giải pháp của em, số người tham dự sau đó đã tăng 150% so với năm trước.

Sử dụng trình tự này, bạn sẽ cung cấp đủ ngữ cảnh để nhà tuyển dụng hiểu được tình hình. Đồng thời, họ sẽ không bị quá tải với những thông tin không liên quan.
2. Những câu hỏi cụ thể với công việc, các tình huống giả định trong tương lai
Người phỏng vấn cũng sẽ quan tâm đến việc bạn sẽ tiếp cận các vấn đề phát sinh như thế nào tại nơi làm việc. Ví dụ:
“Bạn sẽ làm gì nếu chuỗi cung ứng gặp sự cố và dự án của bạn sẽ bị chậm hơn so với thời gian dự kiến?”
“Bạn sẽ làm gì nếu một khách hàng đưa ra khiếu nại?”…
Đối với các doanh nghiệp lớn, ứng viên có thể phải đưa ra giải pháp cho các Case study thực tế mà công ty đã từng gặp phải. Ứng viên sẽ được đặt ra một vấn đề kinh doanh. Nó thường liên quan đến lĩnh vực mà bạn đang làm việc. Sau đó, bạn được yêu cầu đưa ra các hướng để giải quyết vấn đề đó, theo cá nhân hoặc nhóm. Bạn thường được yêu cầu phác thảo các đề xuất của mình dưới dạng bài thuyết trình hoặc dạng viết. Đây sẽ là cơ sở đánh giá khả năng giải quyết vấn đề của ứng viên.
Nhà tuyển dụng thậm chí có thể yêu cầu bạn làm các bài kiểm tra tâm lý để đánh giá kỹ năng. Các bài kiểm tra này tập trung vào khả năng suy nghĩ logic của bạn thông qua các vấn đề về số, không gian hoặc ngôn ngữ. Chúng có thể được sử dụng kết hợp với các bài kiểm tra tính cách để đo lường cả kỹ năng tư duy phản biện và tư duy sáng tạo.
Cải thiện kỹ năng Problem Solving như thế nào?
1. tìm kiếm cơ hội giải quyết các vấn đề ngay trong hoạt động hàng ngày.
Cách tốt nhất để học một kỹ năng là thực hành nó thường xuyên. Vì vậy, việc tiếp xúc với những môi trường tạo cơ hội rèn luyện kỹ năng giải quyết vấn đề như tham gia các CLB, hoạt động nhóm tại trường đại học và hay đi làm chính là những giải pháp tốt nhất.
Một số CLB tại các trường đại học thường tổ chức các sự kiện, cuộc thi dành cho sinh viên. Đây chính là sân chơi để ứng viên rèn luyện khả năng giải quyết vấn đề trong công việc. Một hướng khác để phát triển kỹ năng giải quyết vấn đề chính là đi làm, tiếp xúc với môi trường thực tế. Mỗi sự lựa chọn đều đem lại cho bạn những trải nghiệm và giúp bạn tiếp xúc với các vấn đề cần phải giải quyết.
2. Luyện giải trước các bài tập giải quyết tình huống trong kỳ tuyển dụng
Bất kỳ ứng viên nào đều sẽ phải gặp những tình huống giả định trong kỳ tuyển dụng, đặc biệt khi bạn ứng tuyển vị trí tại các tập đoàn lớn. Để tránh lúng túng, ứng viên nên tìm hiểu về lộ trình ứng tuyển để nắm rõ những thứ cần chuẩn bị cho bản thân.
Trong các cuộc thi Management Trainee tại các tập đoàn đa quốc gia, chắc chắn các ứng viên sẽ đều gặp phải những bài toán kinh doanh thực tế – Business Case tại vòng Assessment Center. Để giảm bớt áp lực và chuẩn bị tốt cho vòng thi, ứng viên phải luyện tập giải case trước để làm quen dần với format, cách suy luận, hướng giải quyết vấn đề,… Các trang chuyên cung cấp tài liệu hoặc những khóa học chính là giải pháp cho vấn đề này. Bạn có thể tham khảo khóa học Case Mastery của Tomorrow Marketers để tìm hiểu kỹ hơn về kỳ tuyển dụng của các đoàn lớn. Ứng viên sẽ được làm quen với các format, các dạng Business/ Marketing Case thường gặp và nắm được mục đích phỏng vấn Case Interview.
Đặc biệt hơn tư duy Problem Solving sẽ được phát triển thông qua những Case Study xuyên suốt khóa học ở 7 ngành hàng khác nhau. Học viên sẽ được cung cấp trọn bộ kiến thức, tư duy và kỹ năng cần thiết từ những giảng viên từng là Quán quân, Ban giám khảo tại các cuộc thi danh tiếng như Nielsen Case Competition hay là Assessor tại các kỳ thi Management Trainee.
3. Trau dồi kiến thức ngành
Thông thường, để giải quyết một vấn đề tại nơi làm việc hoặc trong một tình huống kinh doanh thực tế đòi hỏi kiến thức nhất định về ngành hàng. Một ứng viên sẽ hoang mang trước những vấn đề, rủi ro mà họ không hiểu hoặc không biết cách giải quyết. Hiểu đầy đủ kiến thức về ngành giúp xác định vấn đề chính xác và thu thập thông tin một cách có hệ thống. Từ đó, bạn có thể lập kế hoạch giải quyết hiệu quả. Phát triển kiến thức về ngành chính là cách để phát triển kỹ năng giải quyết vấn đề.
Ví dụ: Bạn là một Marketer tại CloseUp với 2 năm kinh nghiệm. Tình hình kinh doanh của CloseUp hiện đang đi xuống. Cấp trên yêu cầu team Marketing tìm hướng giải quyết cho vấn đề này. Tại cuộc họp, với kiến thức về người dùng và ngành hàng qua các nghiên thị trường trước đây, bạn hiểu rào cản chính của khách hàng đối với việc lựa chọn kem đánh răng là do họ không cảm thấy được sự khác biệt với các sản phẩm cùng loại. CloseUp chưa đủ độc đáo để khách hàng chú ý và lựa chọn.
Vì vậy bạn đưa ra ý kiến tập trung chiến dịch vào giai đoạn củng cố awareness và thúc đẩy việc nhắc mua hàng bằng câu chuyện khác biệt. Ngoài ra, thương hiệu có thể kết hợp hoạt động tại điểm bán để kết nối với khâu chuyển đổi (quà tặng, trưng bày, game,…). Nhờ đây, bạn đã có thể gây ấn tượng với nhà tuyển dụng bằng hiểu biết về ngành, hành vi, insight khách hàng và đưa ra phương án giải quyết nhanh chóng, hợp lý.
4. Tìm hiểu các Framework
Framework chính là chìa khóa giúp bạn giải quyết bài toán kinh doanh một cách nhanh chóng, chính xác và đầy đủ.
Ví dụ, tại vòng Case Interview – hình thức tuyển dụng tại các tập đoàn đa quốc gia:
Các ứng viên sẽ có cơ hội giải quyết Business Case . Nếu chỉ nhận biết được các phương pháp giải Case mà không có khuôn mẫu cũ thể để áp dụng thì sẽ tốn rất nhiều thời gian để giải quyết. Vì vậy, framework trong business chính là nền tảng được sử dụng giúp bạn định hướng tư duy, giải quyết vấn đề một cách có phương pháp, đảm bảo được sự chính xác, khách quan.
Tham khảo thêm một số framework giúp bạn giải các bài toán Business Case : Profitability, 4Ps, 3C, M&A, Porter’s 5 Forces,…
Gây ấn tượng với nhà tuyển dụng trên CV bằng kỹ năng giải quyết vấn đề (Problem Solving)
Thể hiện kỹ năng giải quyết vấn đề cụ thể trong CV là cách để bạn nổi bật hơn so với những ứng viên khác. Thay vì chỉ đơn giản viết rằng bạn có “kỹ năng giải quyết vấn đề tốt”, hãy minh họa cách bạn sử dụng kỹ năng này ở những vị trí trước đây đi kèm các con số cụ thể:
“Giảm 15% chi phí xử lý hàng tồn kho bằng cách sử dụng các phần mềm chuyên dụng:…”
“Giúp tăng 25% mức độ hài lòng của khách hàng bằng cách tạo quy trình chuẩn và các kịch bản để giải quyết các câu hỏi chung”…
Trong ví dụ này, ứng viên đề cập họ có khả năng sử dụng các phần mềm chuyên dụng. Nó cũng ngụ ý rằng họ có kinh nghiệm thực hiện các giải pháp cho một vấn đề.
Có 2 vị trí bạn có thể thể hiện kỹ năng problem solving của bản thân trong CV. Bạn có thể liệt kê chúng tại phần kỹ năng. Đây là nơi bạn liệt kê toàn bộ kỹ năng, từ kỹ năng cứng và kỹ năng mềm. Ngoài ra, phần “kinh nghiệm làm việc” cũng là nơi để giúp bạn thể hiện được khả năng của bản thân. Mặc dù không đề cập rõ ràng từ khoá “giải quyết vấn đề”, nhưng bạn vẫn có thể ngụ ý dưới dạng một số từ khóa giống ví dụ nêu trên để làm nổi bật khả năng của mình. Ngoài ra, ứng viên cần điều chỉnh CV để các kỹ năng giải quyết vấn đề của bạn phù hợp với công việc mà bạn đang ứng tuyển.
Kỹ năng giải quyết vấn đề (Problem Solving) chính là một trong những tiêu chí hàng đầu để đánh giá mỗi ứng viên tại các vòng thi tại các công ty, tập đoàn lớn. Cụ thể hơn, đối với những bạn sinh viên “mơ lớn”, muốn thử thách bản thân tại các tập đoàn đa quốc gia như : Unilever, L’Oréal, Nielsen,… thì các cuộc thi Management Trainee chính là con đường tối ưu nhất .
Và để chinh phục các cuộc thi với tỉ lệ chọi cực cao này, bạn cần trang bị cho bản thân nền tảng vững vàng về tư duy Problem Solving và Marketing để vượt qua các Business Case khó nhằn và tiến đến vòng thi cuối cùng – Final Interview. Nếu bạn mong muốn có một khởi đầu bài bản với những kiến thức về cách tiếp cận, xác định vấn đề và đưa ra nhận định giải quyết đa dạng Business Case một cách linh hoạt, tham gia ngay khóa học Case Mastery tại Tomorrow Marketers nhé!

Bài viết được biên soạn bởi Tomorrow Marketers, vui lòng không sao chép dưới mọi hình thức.
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Creative Problem Solving
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What Is Creative Problem-Solving & Why Is It Important?

- 01 Feb 2022
One of the biggest hindrances to innovation is complacency—it can be more comfortable to do what you know than venture into the unknown. Business leaders can overcome this barrier by mobilizing creative team members and providing space to innovate.
There are several tools you can use to encourage creativity in the workplace. Creative problem-solving is one of them, which facilitates the development of innovative solutions to difficult problems.
Here’s an overview of creative problem-solving and why it’s important in business.
What Is Creative Problem-Solving?
Research is necessary when solving a problem. But there are situations where a problem’s specific cause is difficult to pinpoint. This can occur when there’s not enough time to narrow down the problem’s source or there are differing opinions about its root cause.
In such cases, you can use creative problem-solving , which allows you to explore potential solutions regardless of whether a problem has been defined.
Creative problem-solving is less structured than other innovation processes and encourages exploring open-ended solutions. It also focuses on developing new perspectives and fostering creativity in the workplace . Its benefits include:
- Finding creative solutions to complex problems : User research can insufficiently illustrate a situation’s complexity. While other innovation processes rely on this information, creative problem-solving can yield solutions without it.
- Adapting to change : Business is constantly changing, and business leaders need to adapt. Creative problem-solving helps overcome unforeseen challenges and find solutions to unconventional problems.
- Fueling innovation and growth : In addition to solutions, creative problem-solving can spark innovative ideas that drive company growth. These ideas can lead to new product lines, services, or a modified operations structure that improves efficiency.

Creative problem-solving is traditionally based on the following key principles :
1. Balance Divergent and Convergent Thinking
Creative problem-solving uses two primary tools to find solutions: divergence and convergence. Divergence generates ideas in response to a problem, while convergence narrows them down to a shortlist. It balances these two practices and turns ideas into concrete solutions.
2. Reframe Problems as Questions
By framing problems as questions, you shift from focusing on obstacles to solutions. This provides the freedom to brainstorm potential ideas.
3. Defer Judgment of Ideas
When brainstorming, it can be natural to reject or accept ideas right away. Yet, immediate judgments interfere with the idea generation process. Even ideas that seem implausible can turn into outstanding innovations upon further exploration and development.
4. Focus on "Yes, And" Instead of "No, But"
Using negative words like "no" discourages creative thinking. Instead, use positive language to build and maintain an environment that fosters the development of creative and innovative ideas.
Creative Problem-Solving and Design Thinking
Whereas creative problem-solving facilitates developing innovative ideas through a less structured workflow, design thinking takes a far more organized approach.
Design thinking is a human-centered, solutions-based process that fosters the ideation and development of solutions. In the online course Design Thinking and Innovation , Harvard Business School Dean Srikant Datar leverages a four-phase framework to explain design thinking.
The four stages are:

- Clarify: The clarification stage allows you to empathize with the user and identify problems. Observations and insights are informed by thorough research. Findings are then reframed as problem statements or questions.
- Ideate: Ideation is the process of coming up with innovative ideas. The divergence of ideas involved with creative problem-solving is a major focus.
- Develop: In the development stage, ideas evolve into experiments and tests. Ideas converge and are explored through prototyping and open critique.
- Implement: Implementation involves continuing to test and experiment to refine the solution and encourage its adoption.
Creative problem-solving primarily operates in the ideate phase of design thinking but can be applied to others. This is because design thinking is an iterative process that moves between the stages as ideas are generated and pursued. This is normal and encouraged, as innovation requires exploring multiple ideas.
Creative Problem-Solving Tools
While there are many useful tools in the creative problem-solving process, here are three you should know:
Creating a Problem Story
One way to innovate is by creating a story about a problem to understand how it affects users and what solutions best fit their needs. Here are the steps you need to take to use this tool properly.
1. Identify a UDP
Create a problem story to identify the undesired phenomena (UDP). For example, consider a company that produces printers that overheat. In this case, the UDP is "our printers overheat."
2. Move Forward in Time
To move forward in time, ask: “Why is this a problem?” For example, minor damage could be one result of the machines overheating. In more extreme cases, printers may catch fire. Don't be afraid to create multiple problem stories if you think of more than one UDP.
3. Move Backward in Time
To move backward in time, ask: “What caused this UDP?” If you can't identify the root problem, think about what typically causes the UDP to occur. For the overheating printers, overuse could be a cause.
Following the three-step framework above helps illustrate a clear problem story:
- The printer is overused.
- The printer overheats.
- The printer breaks down.
You can extend the problem story in either direction if you think of additional cause-and-effect relationships.

4. Break the Chains
By this point, you’ll have multiple UDP storylines. Take two that are similar and focus on breaking the chains connecting them. This can be accomplished through inversion or neutralization.
- Inversion: Inversion changes the relationship between two UDPs so the cause is the same but the effect is the opposite. For example, if the UDP is "the more X happens, the more likely Y is to happen," inversion changes the equation to "the more X happens, the less likely Y is to happen." Using the printer example, inversion would consider: "What if the more a printer is used, the less likely it’s going to overheat?" Innovation requires an open mind. Just because a solution initially seems unlikely doesn't mean it can't be pursued further or spark additional ideas.
- Neutralization: Neutralization completely eliminates the cause-and-effect relationship between X and Y. This changes the above equation to "the more or less X happens has no effect on Y." In the case of the printers, neutralization would rephrase the relationship to "the more or less a printer is used has no effect on whether it overheats."
Even if creating a problem story doesn't provide a solution, it can offer useful context to users’ problems and additional ideas to be explored. Given that divergence is one of the fundamental practices of creative problem-solving, it’s a good idea to incorporate it into each tool you use.
Brainstorming
Brainstorming is a tool that can be highly effective when guided by the iterative qualities of the design thinking process. It involves openly discussing and debating ideas and topics in a group setting. This facilitates idea generation and exploration as different team members consider the same concept from multiple perspectives.
Hosting brainstorming sessions can result in problems, such as groupthink or social loafing. To combat this, leverage a three-step brainstorming method involving divergence and convergence :
- Have each group member come up with as many ideas as possible and write them down to ensure the brainstorming session is productive.
- Continue the divergence of ideas by collectively sharing and exploring each idea as a group. The goal is to create a setting where new ideas are inspired by open discussion.
- Begin the convergence of ideas by narrowing them down to a few explorable options. There’s no "right number of ideas." Don't be afraid to consider exploring all of them, as long as you have the resources to do so.
Alternate Worlds
The alternate worlds tool is an empathetic approach to creative problem-solving. It encourages you to consider how someone in another world would approach your situation.
For example, if you’re concerned that the printers you produce overheat and catch fire, consider how a different industry would approach the problem. How would an automotive expert solve it? How would a firefighter?
Be creative as you consider and research alternate worlds. The purpose is not to nail down a solution right away but to continue the ideation process through diverging and exploring ideas.

Continue Developing Your Skills
Whether you’re an entrepreneur, marketer, or business leader, learning the ropes of design thinking can be an effective way to build your skills and foster creativity and innovation in any setting.
If you're ready to develop your design thinking and creative problem-solving skills, explore Design Thinking and Innovation , one of our online entrepreneurship and innovation courses. If you aren't sure which course is the right fit, download our free course flowchart to determine which best aligns with your goals.

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About this Course
This course deals directly with your ability for creativity which is a critical skill in any field. It focuses on divergent thinking, the ability to develop multiple ideas and concepts to solve problems. Through a series of creativity building exercises, short lectures, and readings, learners develop both an understanding of creativity and increase their own ability.
This course will help you understand the role of creativity and innovation in your own work and in other disciplines. It will challenge you to move outside of your existing comfort zone and to recognize the value of that exploration. This course will help you understand the importance of diverse ideas, and to convey that understanding to others. The principal learning activity in the course is a series of "differents" where you are challenged to identify and change your own cultural, habitual, and normal patterns of behavior. Beginning with a prompt, e.g. "eat something different", you will begin to recognize your own = limits and to overcome them. In addition, you are encouraged to understand that creativity is based on societal norms, and that by it's nature, it will differ from and be discouraged by society. In this course, the persistence of the creative person is developed through practice. At the same time, these exercises are constrained by concerns of safety, legality, and economics, which are addressed in their creative process.
Could your company benefit from training employees on in-demand skills?
Instructors

Brad Hokanson, PhD

Jody Nyboer, PhD

University of Minnesota
The University of Minnesota is among the largest public research universities in the country, offering undergraduate, graduate, and professional students a multitude of opportunities for study and research. Located at the heart of one of the nation’s most vibrant, diverse metropolitan communities, students on the campuses in Minneapolis and St. Paul benefit from extensive partnerships with world-renowned health centers, international corporations, government agencies, and arts, nonprofit, and public service organizations.
See how employees at top companies are mastering in-demand skills
Syllabus - What you will learn from this course
Introduction to the course.
Creativity is a skill that can be developed. It requires extensive work by learners, but the lessons, while not conveying traditional content, will change you in ways you do not foresee, but ways which are valuable. The course is a hybrid; it will involve reading, writing, discussions, as well as specific exercises designed to increase and improve your creative skills. You will do work online as well as in the real world; it is designed to be fun and to change your ability for creativity.
Divergent and Convergent Thinking
In this unit we'll look as some of the ways we can describe creativity and examine the concepts of divergent and convergent thinking. We'll look at generating more ideas, how to critique and make improvements, and continue to practice our development of ideas. Practice and exploration continue as these are the means we will continue to improve our own creativity.
Creativity, Motivation and Observation
Sometimes, we need external methods to help us touch all the bases in our creative capability. Here, we'll look at a couple of good methods for helping us generate new ideas.There are a wide range of creativity exercises available; these are but a few. Finding and practicing the development of ideas is an important aspect to becoming more creative.
Creativity and Observation
A lot of the time, creativity can be spurred by something in the environment, triggering connections with new ideas. We react to things we have seen and our experiences; that is from where we build our new ideas.
While much of this course has focused on ways to improve your own creativity, the larger goal of the course is for you to continue to develop your own creativity, in your own way and in your own life. This module continues the development creativity and give you the chance to begin planning your continued development.
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- 4 stars 20.12%
- 3 stars 6.48%
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- 1 star 4.98%
TOP REVIEWS FROM CREATIVE PROBLEM SOLVING
This course makes you stretch your creativity to new lengths as you try new and unusual ideas, Explains how we all can increase our creativity through practice and the practical ways to do so.
I really enjoyed this course, it was very informative and easy to follow. The videos were clear and the graded sections were great. The course as a whole was enjoyable and would recommend to others.
This is really good Course, if we apply creative ideas in our life on our daily basis work in diffrent way...you can understand....How much is easy to live with ppl and family friends....
This course instilled a sense of confidence as well. The tools,techniques and methods used to convey abstract ideas pertaining to creativity were simple and effective.
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Four Obstacles to Creative Problem Solving
Radiology managers face a major issues requiring creative thinking. But these mental blocks can get in the way of problem solving.
How many issues in a week do you encounter that require creative problem solving? When you are in management you encounter a multitude of issues on a weekly basis, some which are very unique.
When a problem arises there are four obstacles I am mindful of that can get in the way of my creative problem solving. The mental obstacles which are referred to as conceptual blocks can constrain the way I look at solving problems and limit the number of solutions I generate.
The four types of conceptual blocks are:
1. Constancy . Constancy means we become committed to one way of looking at a problem and employing one approach to define and solving that problem. The issue with constancy is that since we are creatures of habit we are likely to consistently use the same methodology to our approach in creative problem solving.
2. Commitment . Commitment is seen as a conceptual block because as individuals, once we become committed to an idea or solution we usually follow through with that idea or solution. We become so entrenched in our thinking that we do not consider other alternatives. Studies have shown that commitment has lead to some very silly decisions.
3. Compression . Compression is when we look at a problem in a narrow spectrum and we filter out too much of the relevant information. As problem solvers we must be able to determine what information is factual and important so we can define the problem and develop the best solution.
4. Complacency . Complacency is typically the result of just pure laziness and in most cases can get us in lots of trouble. To solve problems we must ask questions to get the information we need to define the problem and generate the appropriate solution. However, asking individuals questions can raise defense mechanisms which lead to interpersonal conflict and resistance. In addition, asking lots of questions makes us feel as though we come across as not being intelligent. Being inquisitive is important to creative problem solving.
It is important to note that it takes practice to eliminate the tendencies of these four conceptual blocks. I recommend you write them down on a small index card and place the card in your desk.
Here’s a quote from Frank Zappa that I find appropriate for problem solving; “Our mind is like a parachute, it doesn’t work if it is not open.”
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Education for creativity and talent development in the 21st century, threshold effects of creative problem-solving attributes on creativity in the math abilities of taiwanese upper elementary students.
This study aimed to help determine what the typology of math creative problem-solving is. Different from studies that have discussed the threshold effect between creativity and intelligence, this research investigated the threshold effect between creativity and other attributes. The typology of the math creative problem-solving abilities of 409 fifth- and sixth-grade Taiwanese students was identified and compared in this study. A Creative Problem-Solving Attribute Instrument was devised for this study, with the aim of measuring students’ perceptions on their motivation, knowledge, and skills, both in general and in specific domains. Divergent and convergent thinking were also measured. Cluster analyses yielded three creative problem-solving typologies: High, Medium, and Low. The High Attribute group scored significantly higher in the Math Creative Problem-Solving Ability Test than did the Medium Attribute and Low Attribute groups. The results suggest a threshold effect from several attributes—divergent thinking, convergent thinking, motivation, general knowledge and skills, domain-specific knowledge and skills, and environment—on students’ creative problem-solving abilities. Balanced development of attributes may be an important consideration in nurturing creativity in children.
1. Introduction
Creative problem-solving is crucial for the improvement of society and is also important for the activities we do in our daily lives [ 1 , 2 ]. Additionally, creativity and the ability to solve problems creatively are considered essential skills that future talent must be equipped with [ 3 ]. In this study, creativity is a necessary component of creative problem-solving ability. It is therefore necessary to characterize the relationship between problem-solving (in general) and creativity. Creativity can be part of problem-solving [ 4 – 7 ]; it is especially so when solutions to problems are not easily reached or readily available and when the ideas required for solutions are novel and are particularly appropriate to solving the problems [ 8 , 9 ]. Some researchers believe the process of creativity actually constitutes the whole of the problem-solving process, from problem finding to executing a plan [ 10 ]. Guilford [ 11 ] associated creativity with problem-solving and identified four stages of the creative process: (1) recognition of an existing problem; (2) production of a number of relevant ideas; (3) recognition of various possibilities produced; and (4) the drawing of appropriate conclusions that lead to the solution. Houtz [ 12 ] believed that Torrance’s definition of creativity, defined as “the process of sensing gaps or disturbing, missing elements; forming ideas or hypotheses concerning them; testing these hypotheses and communicating the results, possibly modifying and retesting the hypotheses” [ 13 , p. 16], is similar to the process of problem finding and problem-solving, because creativity can be exercised while solving open-ended and ill-defined problems.
It is believed that creative problem-solving ability is difficult to research and that it is difficult to put the results of that research into practice [ 14 ]. Various measures of creativity tend to have different operational definitions, and the attributes of creativity continue to be debated. During the early development of creativity research, the structure of creativity was measured via divergent thinking tests and has gradually come to be equated with divergent thinking [ 11 , 13 ]. However, divergent thinking tests have been evidenced to have poor reliability and weak predictive validity [ 15 ]. Additionally, in some studies, the structure of creativity has been understood as an entity independent from academic achievement, which implies that knowledge and skills learned in school are not necessary in exercising creativity [ 15 – 18 ]. However, with the emergence of the theory of domain specificity of creativity, the importance of knowledge and skills within specific domains has come to be recognized among researchers on creativity [ 19 – 21 ].
The foundation of this research is based on the belief that creativity is multifaceted and complex, and this belief has been evidenced in recent research [ 20 , 22 – 29 ]. Guilford [ 22 ] claimed that several factors are involved in creative thinking: (a) sensitivity to the problem; (b) fluency; (c) novelty; (d) flexibility; (e) ability to synthesize; (f) analytical ability; (g) reorganization or redefinition; (h) complexity; and (i) evaluation. Torrance [ 28 ] discussed the multifaceted nature of creativity, defining creativity as “the process of sensing difficulties, problems, gaps in information, missing elements, something askew; making guesses and formulating hypotheses about these deficiencies; evaluating and testing these guesses and hypotheses; possibly revising and retesting them; and finally communicating the results” (p. 47). Amabile [ 20 , 23 ] suggested a Componential Model of Creativity, which includes domain-relevant skills, creativity-relevant skills, and task motivation. Csikszentmihalyi [ 17 ] proposed six personal resources for producing creativity: intelligence, knowledge, styles of thinking, personality, motivation, and environmental context. Urban’s [ 29 ] component model of creativity views the creative process as containing six components: (1) divergent thinking and acting; (2) general knowledge and base for thinking; (3) specific knowledge base and specific skills; (4) focus and task commitment; (5) motivation and motives; and (6) openness to and tolerance of ambiguity.
Cho [ 24 , 30 ] proposed six attributes of creative problem-solving ability: divergent thinking; convergent thinking; motivation; general knowledge and skills; domain-specific knowledge and skills; and environment, in her Dynamic System Model of Creative Problem-Solving Ability, which was based upon Csikszentmihalyi’s [ 17 ] complex model of creativity and Urban’s [ 29 ] Componential Model of Creativity. Knowledge and skills provide individuals with preliminary resources in which divergent and convergent thinking either evaluate or search for alternatives [ 31 , 32 ]. Divergent thinking is used to search for alternatives. Convergent thinking is used to evaluate various alternatives against criteria and to correct errors in order to achieve the best answer to the problem [ 21 , 33 , 34 ].
Cho suggested that creative problem-solving ability functions like an organic system whose attributes dynamically interact to solve a problem, where motivation, general knowledge and skills, and domain-specific knowledge and skills form the bases of creative problem-solving. Convergent and divergent thinking function as tools that utilize domain-specific and general knowledge and skills in order to solve problems in a new and useful fashion. Creative problem-solving ability can grow or diminish, depending on the micro- and macro-environmental conditions of the external organic systems individuals find themselves in. In addition, if any of the attributes are not developed to the necessary level, creativity will not blossom. Cho’s model is the theory upon which this study is founded.
The threshold effect is one of the essential topics discussed in creativity research, and the correlation between creativity and intelligence is also often investigated. Creativity and creative problem-solving have also been stated to be related to intelligence [ 21 ]. The theory of the threshold effect for intelligence and creativity was first proposed by Guilford, who stated that creativity is well-predicted at IQ levels below 120 but not above 120 [ 21 ]. However, even when creativity is recognized as multifaceted and cannot be simply determined by a single factor, the threshold effect theory has merely been studied as it relates to intelligence and creativity but not applied to the correlations between creativity and other attributes. Torrance [ 13 ] claimed threshold effects in intelligence, but such effects have not yet been verified for other attributes of creativity.
In this study, the Creative Problem-Solving Attributes Inventory (CPSAI) was developed by combining Cho’s dynamic system model [ 23 , 24 , 30 ] and Treffinger’s CPS Model Version 4.0 [ 35 , 36 ] as frames of reference. Version 4.0 of Treffinger’s CPS emphasizes a three-stage process of solving problems creatively, where divergent thinking and convergent thinking are both utilized at each stage [ 35 , 36 ]. The three overall stages of the CPS process are as follows: understanding the problem (mess-finding, data-finding, and problem finding); generating ideas (idea-finding); and planning for action (solution-finding and acceptance-finding) [ 37 ]. Although it is not the latest version, CPS Version 4.0 clearly describes the creative problem-solving processes that young students, who are relatively inexperienced real-life problem solvers, might experience. It also does so in a less complex manner than is detailed in CPS Version 6.1, the latest one.
The main purpose of this study was to shed light on the essential attribute(s) of creative problem-solving ability in math, as based on Cho’s theory. Most importantly, the study aimed to investigate whether there is a typology, or even a threshold effect, between creative problem-solving and a variety of attributes, among different levels of creative math problem-solving ability. This study aimed to provide insight into how best to nurture creativity.
2. Materials and Methods
2.1. sample.
A total of 409 fifth and sixth graders were recruited from two elementary schools in Taiwan. Because there is a minimum age requirement for Taiwanese students to enroll in elementary school and there is no accelerated program at the elementary level, fifth- and sixth-grade students’ ages generally range from 10 to 12 years. 325 students (54.8% males and 45.2% females) were sampled from School A. In School B, a sample of 84 students (60.7% males and 39.3% females) participated. Demographically, these participants came from two-parent households (96%), were born in Taiwan (99%), and mainly spoke either Mandarin (59%) or Taiwanese (37%) at home.
2.2. Research Questions
The following research questions were addressed in this study: (i) How are the proposed attributes in Cho’s theory related to corresponding attributes assessed by other established measures (e.g., the Creativity Assessment Packet, Critical Thinking Test, and Inventory of Parental Influence)? (ii) What are the distinctive patterns of attribute combinations for creative problem-solving ability evidenced among fifth- and sixth-grade Taiwanese students? (iii) After categorizing the respondents into three different groups based on their responses to the CPSAI, what were the differences between these three groups, in terms of their math creative problem-solving performance?
2.3. Instruments
The CPSAI is an instrument that measures students’ self-perceptions of five attributes of creative problem-solving ability. To examine its structural validity, four other instruments were also administered: the Math Creative Problem-Solving Ability Test [ 26 ]; the Creativity Assessment Packet [ 38 ]; the Critical Thinking Test-I [ 39 ]; and the Inventory of Parental Influence [ 40 ]. The validity and reliability of each instrument are described below.
The CPSAI . The CPSAI is a self-report questionnaire in which students rate their frequency of using attributes of creative problem-solving, by responding to 41 items on a scale from 1 (Hardly Ever) to 5 (Very Often) . The theoretical basis of the CPSAI is adopted from Cho’s Dynamic System Model of Creative Problem-Solving and Treffinger’s Creative Problem-Solving [ 23 , 35 ]. There are five subscales included: Divergent Thinking; Convergent Thinking; Motivation; General Knowledge; and Environment. In each of the five subscales, the test questions describe possible behaviors for creative problem-solving attributes that can be exhibited during each stage of creative problem-solving. For instance, items in the Divergent Thinking subscale describe divergent thinking-related behaviors in the stages of problem finding (e.g., “I ask many related questions when I try to understand problems”), generating ideas (e.g., “I get many different ideas by thinking from different standpoints”), and planning for action (e.g., “I have several different procedures to solve problems”).
Because the CPSAI is a new measure and the Math Creative Problem-Solving Ability Test (MCPSAT) is a slightly modified version of the original, these instruments were first piloted over a one-month period to establish reliability. Detailed information about the MCPSAT can be found in the next paragraph. The pilot group consisted of 74 students (31 fifth graders and 43 sixth graders) from various backgrounds, recruited from several private institutions across Tainan City and Tainan County. Cronbach’s alpha for the test items showed reasonable internal-consistency on the subscales of Motivation , Environment , Divergent Thinking , and Convergent Thinking but only minimally adequate reliability on the subscale of General Knowledge and Skills .
The Math Creative Problem-Solving Ability Test (MCPSAT) . The MCPSAT is a creative problem-solving ability assessment of open-ended math problems that identifies gifted students in math [ 25 ]. Students’ responses were evaluated in terms of fluency, flexibility, and originality [ 26 ]. Fluency is scored according to the number of correct answers to the problems. Flexibility is scored by the number of categories of correct answers produced for the problems. For instance, one of the questions is, “Using the following equation ( ), please create up to 10 new equations.” If a student’s answer includes and , this would be considered as two different categories. Originality is scored by how frequently a student’s given correct answer to a question was provided by the other students (i.e., more frequent answers equal lower originality). A rubric with exemplary answers for each score ranking was developed by selecting and classifying all relevant responses to each question. The members of the research team discussed and revised the evaluation rubrics when faced with unique and challenging responses. Participants’ responses were scored by math teachers who have been trained on the nature of the problems and on possible answers for each test item. Taiwanese math teachers reviewed the problems in terms of their difficulty, with comparative reference to the Taiwanese math curriculum, and noted students’ difficulties during the pilot testing, resulting in the selection of eight problems (five easy items, two medium items, and one difficult item) for the final version of the MCPSAT for the study.
Statistical analyses were performed to examine the following aspects of the MCPSAT with regard to the current participants: internal-consistency reliability; internal validity; and difficulty level. Reliability, measured by internal-consistency, of the MCPSAT was found to be reasonably good, since Cronbach’s alpha for the eight test items was .73. The internal validity of each test item was calculated using BIGSTEPS, and an item analysis was conducted based on Rasch’s 1-parameter item-response model. The analysis model used in this study was the Partial Credit Model. The value for item 8 exceeded 2.0, which indicated low internal validity (see Table 1 ). Aside from item 8, all other internal validity indexes were less than 1.2. The overall fit statistics confirmed that the internal values of the items were high enough to be good. In this study, the item difficulty was calculated based on Rasch’s 1-parameter item-response model. An item difficulty of 0.0 indicated average item difficulty. The higher the value, the more difficult the item. Results showed that the logit scores of items 7 and 8 were the most difficult items (see Table 1 ) and that the test items had been distributed from easy to difficult. Additionally, when all the items are distributed equally from easy to difficult, the ordering of the problems itself may motivate the participants to attempt and complete all of the problems in the instrument, rather than placing more difficult obstacles in their paths earlier on.
The Creativity Assessment Packet (CAP) . The original version of the CAP was created by Williams [ 38 ]. Its Chinese version was translated and validated by Lin and Wang. The CAP is intended to identify creativity levels among students in grades 4 to 12 [ 41 ]. The two subtests of the CAP—the Test of Divergent Thinking (TDT) and the Test of Divergent Feeling (TDF)—were investigated for relationships with the Divergent Thinking and Motivation subscales measured by the CPSAI, respectively. In the TDT, examinees completed drawing 12 different figures, based on the lines presupplied in each item, and gave titles to their drawings. Their final products were scored based on fluency, flexibility, originality, collaboration, openness, and title. The TDF is a 3-point Likert scale questionnaire that asks students’ preference on statements in four subscales: curiosity; risk taking; desire for complexity; and imagination.
In this study, 31 students’ responses were randomly selected and rated by an external rater to test the interrater reliability of the TDT, which was found to reach .91. Additionally, the alpha value for internal-consistency was .85 for the TDF and .64 for the TDT. The overall score on the TDT significantly correlated with the subscale scores for fluency ( , ), originality ( , ), openness ( , ), elaboration ( , ), and titles ( , ), but not with flexibility.
The Critical Thinking Test- (CTT-) I . The CTT-I measures critical thinking skills of 5th- to 12th-grade students, with 25 multiple-choice questions that represent five critical thinking skills (Identification of Assumptions; Induction; Deduction; Interpretation; and Evaluation of Arguments) [ 39 ]. The test has previously been validated with 2,228 elementary students, and the alpha, using the ITEMAN item analysis, was .76. Cronbach’s alpha for each subscale ranged from .32 to .49. Correlations between the overall score and the subscale scores ranged from .23 to .45 . In this study, Cronbach’s α of the overall test was .57. The overall score of the CTT-I significantly correlated with Identification of Assumptions ( , ); Induction ( , ); Deduction ( , ); Interpretation ( , ); and Evaluation of Arguments ( , ).
The Inventory of Parental Influence (IPI) . The IPI is a cross-cultural, self-reported instrument designed to identify students’ perceptions of family processes, including parental pressure; support; help; pressure toward intellectual development; monitoring; and communication [ 40 ]. A positive family process has been found to significantly influence students’ creative problem-solving ability [ 42 ]. In addition, support and pressure toward intellectual development have been observed to significantly affect former Science Olympians’ academic achievements [ 42 ]. Cho and Campbell [ 42 ] validated the instrument with 757 past Science Olympians and obtained internal-consistency reliability for the scales of support and of pressure toward intellectual development .
In this study, the relationships between the Environment subscale of the CPSAI and the subscales of Pressure toward Intellectual Development and of Support were investigated. This is because a positive family process, which consists of support and pressure toward intellectual development, is significantly correlated with creative problem-solving in math [ 43 ]. In this study, the internal-consistencies of the Support and Pressure toward Intellectual Development subscales were and , respectively.
In summary, the TDT and TDF subtests of the CAP, the CTT-I, and the IPI were administered to determine whether the attributes measured by the CPSAI subscales are similar to those measured by these established instruments. Scores on general and domain-specific knowledge and skills measured by the CPSAI were compared with students’ GPAs and academic achievements, respectively.
2.4. Data Collection
The MCPSAT, CPSAI, CAP, CTT-I, and IPI were administered during two one-hour sessions over two weeks, with the MCPSAT and CPSAI in the first week and the CAP, CTT-I, and IPI in the second week. All instruments were administered by the author, with assistance from teachers at the schools. Students’ math achievement test scores, which are administered three times per semester, and GPAs from the previous semester were used as measures of domain-specific and general knowledge and skills.
2.5. Data Analysis
A confirmatory factor analysis was performed to determine if the relationships between the variables in Cho’s model resemble the relationships between the variables in the observed data. In addition, internal-consistency between the overall scores and the score for each subscale of the CPSAI items and correlation coefficients among the subscale scores were analyzed. The correlation coefficients between the sub-scores and total score of the CPSAI were computed. Additionally, the scores from the CAP, CTT-I, and IPI were analyzed in comparison with the respective subscales of the CPSAI. A cluster analysis based on participants’ responses on the CPSAI was performed to determine the typical typology of creative problem-solving ability in Taiwanese students. An analysis of variance (ANOVA) and follow-up post hoc tests were carried out to investigate the mean differences in the five attributes (divergent thinking; convergent thinking; motivation; general knowledge; and environment) and to investigate differences in the scores on the MCPSAT between the clusters.
3.1. Structural Validity and Reliability
Confirmatory factor analysis was conducted to examine if the hypothesized five-factor structure, which was believed to underlie the factors in the CPSAI, fits the data. Hypothesized models were assessed by AMOS maximum likelihood factor analysis and evaluated for four measures of fit: (a) chi-square test; (b) Comparative Fit Index (CFI); (c) Normed Fit Index (NFI); and (d) Root Mean Square Error of Approximation (RMSEA).
The Divergent Thinking scale showed a good fit ( (35, 281), , CFI = .960, NFI = .923, and RMSEA = .058). The Convergent Thinking scale moderately fit the observed data ( (20, 281), , CFI = .935, NFI = .914, and RMSEA = .101). The model for the Motivation scale was a reasonably good fit ( (9, 281), , CFI = .983, NFI = .960, and RMSEA = .050). There was a good fit for the hypothesized model for General Knowledge and Skills ( (5, ), , CFI = 1.00, NFI = .992, and RMSEA = .000). For the Environment scale , the chi-square yielded an undesirable value ( (44, ), ), but a moderate fit with the observed data was seen (CFI = .924, NFI = .897, and RMSEA = .094). Overall, the findings of the confirmatory factor analysis yielded a good to moderate fit between the five-factor structure model and the observed data.
Correlation coefficients were computed for the five subscales. Tables 2 and 3 present the means and standard deviations, as well as the correlational analysis in which statistically significant correlations ranged from .45 to .70 . The correlation between the Divergent Thinking and Convergent Thinking scales was the highest ( , ). The Motivation scale correlated higher with Divergent Thinking ( , ) and Convergent Thinking ( , ) compared to General Knowledge and Skills ( , ) and Environment ( , ). In terms of the relationship between the overall CPSAI score and each subscale, Divergent Thinking ( , ) and Convergent Thinking ( , ) correlated higher with the CPSAI total score, while Environment ( , ), Motivation ( , ), and General Knowledge and Skills ( , ) appeared to be slightly less correlated.
To assess whether the items for each scale yielded reliable data, Cronbach alphas were computed. The alpha values for Divergent Thinking , Convergent Thinking , Environment , Motivation , and General Knowledge and Skills indicated that their respective items had good internal-consistency. Furthermore, the internal-consistency of the items overall was good .
3.2. Relationship between CPS Attributes and the Established Instruments
The Pearson correlation coefficients between Divergent Thinking and TDT ( , ), Convergent Thinking and the CTT-I ( , ), Motivation and the TDF ( , ), Environment and positive IPI I ( , ), and General Knowledge and Skills and academic achievement ( , ) indicated that the scores on the established instruments and academic achievement were related to the scores on the attributes of CPSAI. Medium to large effect sizes were found in the associations. The correlation coefficient between the Divergent Thinking scale of CPSAI and the TDT was the lowest. The content of the Divergent Thinking scale of the CPSAI measures math problem-solving situations, whereas the TDT measures divergent thinking in drawing figures.
3.3. Differences in Attributes among Different Math Creativity Groups
A hierarchical cluster analysis was performed to identify relatively homogenous groups, based on students’ responses in the scales of Divergent thinking, Convergent thinking, Motivation, General Knowledge and Skills , and Environment . After excluding missing values, 73% of the samples were included in the cluster analysis. Three clusters were found to be the most appropriate, as they yielded the most statistically significant differences among the clusters. These three clusters were eventually (see below) labeled Low, Medium, and High.
A one-way ANOVA was conducted to examine the differences in the five attributes among the three clusters. Levene tests on the first one-way ANOVA were significant for the subscales of Divergent Thinking and Motivation , which indicated violations of the assumption of homogeneity of variances. Therefore, Games-Howell tests were performed for these two subscales, whereas Tukey HSD tests were conducted for the subscales of Convergent Thinking, Environment , and General Knowledge and Skills .
Table 4 shows statistically significant differences between the three clusters in Convergent Thinking ( , ), Environment ( , ), and General Knowledge and Skills ( , ) . The means for Convergent Thinking, Environment, General Knowledge and Skills, Divergent Thinking , and Motivation in Cluster 3 were the highest among the three clusters, whereas Cluster 1 showed the lowest means across all five attributes. Post hoc Tukey tests indicated that the mean differences between pairs of clusters were significant in each of these five subscales . Clusters 1, 2, and 3 were labeled as Low Attribute (LA), Medium Attribute (MA), and High Attribute (HA) based on their mean scores in all five subscales (see Figure 1 ). The High Attribute (HA) group had at least above medium levels in Divergent Thinking, Convergent Thinking, Environment , and General Knowledge . In addition, the HA students tended to have very high motivation when solving new and difficult problems. On the other hand, mean scores of the Low Attribute (LA) group were the lowest in each subscale among the three clusters. Furthermore, the HA students showed higher scores in Motivation than did the MA and LA students. Students in the Medium Attribute (MA) group had higher levels of each attribute than those in the LA group but had lower levels in Divergent Thinking, ConvergentThinking , Motivation , Environment , and Knowledge than did those in the HA group.

Significant differences were found among the three clusters in their MCPSAT scores, F (2, 290) = 9.69, (see Table 5 ). The HA students scored highest on the MCPSAT and the LA students scored the lowest. Post hoc Tukey tests indicated that the HA group significantly differed from the MA and LA students, while differences between the LA and MA groups were insignificant.
4. Discussion
This study aimed to investigate typology of different creative problem-solving groups. A newly devised instrument, the CPSAI, with five different subscales ( Divergent Thinking ; Convergent Thinking ; Motivation ; General Knowledge ; and Environment ), was utilized in this study. Several analyses were computed to investigate the reliability and validity of the CPSAI, as well as its correlation with established instruments such as the MCPSAT, CAP, CTT-I, and IPI. Those instruments measure creative problem-solving in math, divergent thinking, convergent thinking, and family processes, respectively.
According to the results of the confirmatory factor analysis, most of the subscales yielded a reasonable fit, save for the Convergent Thinking scale. Further clarification may be needed for items measuring convergent thinking, such as rephrasing them in a way that allows examinees to understand them more readily. In addition, there have been studies indicating the importance of domain-specific knowledge in creativity [ 20 , 23 ]. Therefore, the concept of domain specificity may need to be incorporated into the test questions for convergent thinking, motivation, and divergent thinking in the CPSAI in the future. As Brophy [ 34 ] pointed out, individuals constantly alternate between ideation and evaluation during the creative problem-solving process, such that these two types of cognitive thinking may work in a “zigzag pattern.” This may have caused difficulty for the participating fifth and sixth graders in distinguishing between the divergent and convergent thinking processes. Divergent thinking and convergent thinking may not be processes that are exclusive of each other. While an individual explores alternatives, convergent thinking is also required to evaluate previous solutions or ideas and, based on the evaluation results, they will continue to or stop searching for new alternatives [ 34 ]. Future research may need to be conducted, with participants with higher levels of cognitive maturity.
Values for internal-consistency on each subscale ranged from .79 to .89, indicating good reliability. Further, the items interrelated well enough to be summed as a composite variable, and each of the five factors was measured well by its subscale items. The subscales statistically correlated with each other, ranging from .45 to .70, suggesting moderate to high relationships between them. The structures of the subscales shared some common ground yet were unique from each other, confirming Cropley’s claim that these two types of cognitive processes (convergent and divergent thinking) are both used to generate ideas, but in different fashions [ 29 ]. Divergent Thinking and Convergent Thinking were the most highly correlated among the subscales. This corresponds to the results of the factor analysis, which revealed that these two concepts were not easily distinguished by the participants.
The results of the correlation analyses between the scores on the subscales and established instruments ranged between .20 and .60, signifying medium to large relationships, suggesting that there are similarities as well as differences between the subscales of the CPSAI and the other established instruments. For example, the Divergent Thinking scale had a significant but low correlation with TDT. This result can be explained by the domain specificity of creativity and divergent thinking. Baer theorized that creativity is domain-specific, such that creativity in one field cannot be transferred to another field, based on the low correlations among products in five tasks (telling stories; writing stories; writing poems; writing mathematical word problems; and making collages) [ 44 – 46 ]. In other words, an individual’s creativity in drawing figures as tested in the TDT may not transfer to creativity in solving math problems.
The cluster analysis yielded three patterns of attributes, with the HA group having the highest mean scores across all of the attributes, followed by the MA group, and then the LA group. In addition, participants in the HA group acquired the highest scores on the MCPSAT, followed by students in the MA and LA groups, respectively. Although the three groups significantly differed from each other across attributes, only the MCPSAT score of the HA group was significantly different from the other two groups; the MA and LA groups had similar scores on the MCPSAT. This implies that there might be a threshold effect required for attributes in creative problem-solving to have an impact. In other words, unless students have at least a threshold level (the midpoint of the 5-point scale) in all of the attributes, differences in these attributes below the threshold level do not result in a difference in actual creative problem-solving.
This empirical finding of the present study supports Cho’s Dynamic System Model of Creative Problem-Solving Ability [ 23 , 24 , 30 ], in which all attributes of creative problem-solving are equally important and have to be adequately developed before superior creativity can manifest. More importantly, these results imply the importance of balanced development among attributes. No particular attribute stands out from the rest. Instead, attributes of creative problem-solving need to be developed equally to certain levels, as supported by Cho, who claimed that not only do attributes of creative problem-solving interact with each other to help solve problems in a creative manner during the process, but also creative problem-solving is an organic system that cannot develop properly without the balanced development of these attributes [ 24 ]. Therefore, two principles in the nurturing and development of creative problem-solving are as follows: (a) all attributes are equally important and (b) these attributes must all be developed to a certain level in order for an individual to perform creative problem-solving [ 47 ]. Moreover, past studies have discussed the threshold theory with regard to intelligence and creativity [ 48 – 50 ], but not the threshold theory’s effect on other specific attributes. Therefore, these current findings should be further investigated to determine their generalizability.
5. Conclusion
In this evolving environment, creative problem-solving is essential for human beings to solve the complex challenges we face [ 3 ]. It is critical to equip our children with creative problem-solving abilities. This study investigated the typology of math creative problem-solving ability. Most importantly, the results of this study may have shown a threshold effect for creative problem-solving attributes, meaning that one has to achieve a certain level in divergent thinking, convergent thinking, motivation, environment, and knowledge and skills in order for them to have an impact on creative problem-solving ability. This study showed that the attributes in Cho’s [ 23 , 24 , 30 ] model are equally important and need to be developed equally to certain levels, thus contributing to the existing knowledge regarding creative problem-solving.
Conflicts of Interest
The author declares that there are no conflicts of interest regarding publishing this paper.
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Giải quyết vấn đề sáng tạo (Creative Problem Solving)
Tìm hiểu những kỹ thuật và chiến lược giải quyết vấn đề (problem solving) có thể giúp bạn xử lý hiệu quả những thách thức bạn gặp phải trong
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