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Learning to paraphrase supports both writing ability and reading comprehension, particularly for less skilled learners. As such, educational tools that integrate automated evaluations of paraphrases can be used to provide timely feedback to enhance learner paraphrasing skills more efficiently and effectively. Paraphrase identification is a popular NLP classification task that involves establishing whether two sentences share a similar meaning. Paraphrase quality assessment is a slightly more complex task, in which pairs of sentences are evaluated in-depth across multiple dimensions. In this study, we focus on four dimensions: lexical, syntactical, semantic, and overall quality. Our study introduces and evaluates various machine learning models using handcrafted features combined with Extra Trees, Siamese neural networks using BiLSTM RNNs, and pretrained BERT-based models, together with transfer learning from a larger general paraphrase corpus, to estimate the quality of paraphrases across the four dimensions. Two datasets are considered for the tasks involving paraphrase quality: ULPC (User Language Paraphrase Corpus) containing 1998 paraphrases and a smaller dataset with 115 paraphrases based on children’s inputs. The paraphrase identification dataset used for the transfer learning task is the MSRP dataset (Microsoft Research Paraphrase Corpus) containing 5801 paraphrases. On the ULPC dataset, our BERT model improves upon the previous baseline by at least 0.1 in F1-score across the four dimensions. When using fine-tuning from ULPC for the children dataset, both the BERT and Siamese neural network models improve upon their original scores by at least 0.11 F1-score. The results of these experiments suggest that transfer learning using generic paraphrase identification datasets can be successful, while at the same time obtaining comparable results in fewer epochs.